Geometric and Functional Analysis最新文献

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Affirmative Resolution of Bourgain’s Slicing Problem Using Guan’s Bound 用关界肯定解Bourgain的切片问题

IF 2.2 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis

Pub Date : 2025-09-01 DOI: 10.1007/s00039-025-00718-w

Boaz Klartag, Joseph Lehec

We provide the final step in the resolution of Bourgain’s slicing problem in the affirmative. Thus we establish the following theorem: for any convex body $K subseteq mathbb{R}^{n}$ of volume one, there exists a hyperplane $H subseteq mathbb{R}^{n}$ such that

Vol_{n-1}(K cap H) > c, $Vol_{n-1}(K cap H) > </div> </div> <div class="substance_2 ccn" data-abstract-lang="cn"> <input id="exp1_cn_0" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_cn_0"></label> 我们给出了解决布尔甘切片问题的最后一步。因此，我们建立了以下定理：对于卷1的任意凸体K subseteq mathbb{R}^{n}K subseteq mathbb{R}^{n}，存在一个超平面H subseteq mathbb{R}^{n}H subseteq mathbb{R}^{n}使得Vol_{n-1}(K cap H) > c, Vol_{n-1}(K cap H) bbb_c，其中c &gt； 0c > 0是一个泛常数。我们的证明结合了Milman的mm -椭球理论，Guan的随机局部化和最近的边界，以及Eldan和Mikulincer对Shannon-Stam不等式的稳定性估计。 </div> </div> <div class="wxicon"> <button class="buttonicon svgimg" onclick="logintishi(this);"> <img src="/Content/css/sci/svg/pdfl.svg" alt="求助PDF" /><em class="icontext">求助PDF</em> </button> <div style="display:none;">{"title":"Affirmative Resolution of Bourgain’s Slicing Problem Using Guan’s Bound","authors":"Boaz Klartag, Joseph Lehec","doi":"10.1007/s00039-025-00718-w","DOIUrl":"https://doi.org/10.1007/s00039-025-00718-w","url":null,"abstract":"<p>We provide the final step in the resolution of Bourgain’s slicing problem in the affirmative. Thus we establish the following theorem: for any convex body <span><span style=\"\">K subseteq mathbb{R}^{n}</span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.313ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -778.3 3470.7 995.9\" width=\"8.061ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-4B\" y=\"0\"></use><use x=\"1167\" xlink:href=\"#MJMAIN-2286\" y=\"0\"></use><g transform=\"translate(2223,0)\"><use x=\"0\" xlink:href=\"#MJAMS-52\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1021\" xlink:href=\"#MJMATHI-6E\" y=\"581\"></use></g></g></svg></span><script type=\"math/tex\">K subseteq mathbb{R}^{n}</script></span> of volume one, there exists a hyperplane <span><span style=\"\">H subseteq mathbb{R}^{n}</span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.309ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -777 3469.7 994.3\" width=\"8.059ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-48\" y=\"0\"></use><use x=\"1166\" xlink:href=\"#MJMAIN-2286\" y=\"0\"></use><g transform=\"translate(2222,0)\"><use x=\"0\" xlink:href=\"#MJAMS-52\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1021\" xlink:href=\"#MJMATHI-6E\" y=\"581\"></use></g></g></svg></span><script type=\"math/tex\">H subseteq mathbb{R}^{n}</script></span> such that </p><span><span style=\"\"> Vol_{n-1}(K cap H) &gt; c, </span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.614ex\" role=\"img\" style=\"vertical-align: -0.706ex;\" viewbox=\"0 -821.4 8697.5 1125.3\" width=\"20.201ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-56\" y=\"0\"></use><use x=\"769\" xlink:href=\"#MJMATHI-6F\" y=\"0\"></use><g transform=\"translate(1255,0)\"><use x=\"0\" xlink:href=\"#MJMATHI-6C\" y=\"0\"></use><g transform=\"translate(298,-150)\"><use transform=\"scale(0.707)\" x=\"0\" xlink:href=\"#MJMATHI-6E\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"600\" xlink:href=\"#MJMAIN-2212\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1379\" xlink:href=\"#MJMAIN-31\" y=\"0\"></use></g></g><use x=\"2982\" xlink:href=\"#MJMAIN-28\" y=\"0\"></use><use x=\"3372\" xlink:href=\"#MJMATHI-4B\" y=\"0\"></use><use x=\"4483\" xlink:href=\"#MJMAIN-2229\" y=\"0\"></use><use x=\"5373\" xlink:href=\"#MJMATHI-48\" y=\"0\"></use><use x=\"6261\" xlink:href=\"#MJMAIN-29\" y=\"0\"></use><use x=\"6929\" xlink:href=\"#MJMAIN-3E\" y=\"0\"></use><use x=\"7985\" xlink:href=\"#MJMATHI-63\" y=\"0\"></use><use x=\"8419\" xlink:href=\"#MJMAIN-2C\" y=\"0\"></use></g></svg></span><script type=\"math/tex; mode=display\"> Vol_{n-1}(K cap H) >","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"28 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}</div> <span class="citeNo" data-field="citation" data-doi="10.1007/s00039-025-00718-w">引用次数: 0</span> <button class="buttonicon" name="dangeyinyong" onclick="dangeyinyong(this);"> <img src="/Content/css/sci/svg/yy.svg" alt="引用" /> <em class="icontext">引用</em> </button> <button class="buttonicon" name="piliangyinyong" attr-id="0" attr-doi="10.1007/s00039-025-00718-w" attr-title="Affirmative Resolution of Bourgain’s Slicing Problem Using Guan’s Bound" attr-citationcount="0" onclick="piliangyinyong(this);"> <img src="/Content/css/sci/svg/plyy.svg" alt="批量引用" /> <em class="icontext">批量引用</em> </button> </div> </div> <div class="sslist"> <a class="caption cen" data-title-lang="en" href="/literature/144924668.htm">Semiclassical Measures for Complex Hyperbolic Quotients</a> <a class="caption ccn" data-title-lang="cn" href="/literaturecn/144924668.htm" attr-paper="paper" attr-paperid="144924668">复双曲商的半经典测度</a> <div class="substance"> <span class="IF1" attr-if="if">IF 2.2 </span> <span class="fq1" attr-fq="fq">1区数学</span> <span class="qe1" attr-qe="qe">Q1 MATHEMATICS</span> <div class="journal"> <a href="/journal/12478.htm" target="_blank" data-id="12478" data-field="ja"><em>Geometric and Functional Analysis</em></a> </div> <span class="Pub">Pub Date : 2025-08-28</span> <span class="Pub">DOI: 10.1007/s00039-025-00717-x</span> </div> <div class="author" data-author="true" data-paperid="144924668">Jayadev Athreya, Semyon Dyatlov, Nicholas Miller</div> <div class="substance_2 cen" data-abstract-lang="en"> <input id="exp1_1" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_1"></label> <p>We study semiclassical measures for Laplacian eigenfunctions on compact complex hyperbolic quotients. Geodesic flows on these quotients are a model case of hyperbolic dynamical systems with different expansion/contraction rates in different directions. We show that the support of any semiclassical measure is either equal to the entire cosphere bundle or contains the cosphere bundle of a compact immersed totally geodesic complex submanifold.</p><p>The proof uses the one-dimensional fractal uncertainty principle of Bourgain–Dyatlov (Ann. Math. (2) 187(3):825–867, 2018) along the fast expanding/contracting directions, in a way similar to the work of Dyatlov–Jézéquel (Ann. Henri Poincaré, 2023) in the toy model of quantum cat maps, together with a description of the closures of fast unstable/stable trajectories relying on Ratner theory.</p> </div> </div> <div class="substance_2 ccn" data-abstract-lang="cn"> <input id="exp1_cn_1" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_cn_1"></label> 研究紧复双曲商上拉普拉斯特征函数的半经典测度。这些商圈上的测地线流动是在不同方向上具有不同膨胀/收缩速率的双曲动力系统的一个模型。我们证明了任何半经典测度的支持要么等于整个球束，要么包含紧致浸没的完全测地线复子流形的球束。该证明采用了布尔格因-迪亚特洛夫（Bourgain-Dyatlov）的一维分形不确定性原理。数学。（2) 187(3): 825-867, 2018）沿着快速扩张/收缩方向，以类似于dyatlov - jsamzquel (Ann。Henri poincar<e:1>, 2023)在量子猫映射的玩具模型中，以及依赖于拉特纳理论的快速不稳定/稳定轨迹闭包的描述。 </div> </div> <div class="wxicon"> <button class="buttonicon svgimg" onclick="logintishi(this);"> <img src="/Content/css/sci/svg/pdfl.svg" alt="求助PDF" /><em class="icontext">求助PDF</em> </button> <div style="display:none;">{"title":"Semiclassical Measures for Complex Hyperbolic Quotients","authors":"Jayadev Athreya, Semyon Dyatlov, Nicholas Miller","doi":"10.1007/s00039-025-00717-x","DOIUrl":"https://doi.org/10.1007/s00039-025-00717-x","url":null,"abstract":"<p>We study semiclassical measures for Laplacian eigenfunctions on compact complex hyperbolic quotients. Geodesic flows on these quotients are a model case of hyperbolic dynamical systems with different expansion/contraction rates in different directions. We show that the support of any semiclassical measure is either equal to the entire cosphere bundle or contains the cosphere bundle of a compact immersed totally geodesic complex submanifold.</p><p>The proof uses the one-dimensional fractal uncertainty principle of Bourgain–Dyatlov (Ann. Math. (2) 187(3):825–867, 2018) along the fast expanding/contracting directions, in a way similar to the work of Dyatlov–Jézéquel (Ann. Henri Poincaré, 2023) in the toy model of quantum cat maps, together with a description of the closures of fast unstable/stable trajectories relying on Ratner theory.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"27 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}</div> <span class="citeNo" data-field="citation" data-doi="10.1007/s00039-025-00717-x">引用次数: 0</span> <button class="buttonicon" name="dangeyinyong" onclick="dangeyinyong(this);"> <img src="/Content/css/sci/svg/yy.svg" alt="引用" /> <em class="icontext">引用</em> </button> <button class="buttonicon" name="piliangyinyong" attr-id="1" attr-doi="10.1007/s00039-025-00717-x" attr-title="Semiclassical Measures for Complex Hyperbolic Quotients" attr-citationcount="0" onclick="piliangyinyong(this);"> <img src="/Content/css/sci/svg/plyy.svg" alt="批量引用" /> <em class="icontext">批量引用</em> </button> </div> </div> <div class="sslist"> <a class="caption cen" data-title-lang="en" href="/literature/144924667.htm">CG10543 Protein Is Involved in the Regulation of Transcription of Ecdysone-Dependent Genes</a> <a class="caption ccn" data-title-lang="cn" href="/literaturecn/144924667.htm" attr-paper="paper" attr-paperid="144924667">CG10543蛋白参与调控蜕皮激素依赖基因的转录</a> <div class="substance"> <span class="IF1" attr-if="if">IF 2.2 </span> <span class="fq1" attr-fq="fq">1区数学</span> <span class="qe1" attr-qe="qe">Q1 MATHEMATICS</span> <div class="journal"> <a href="/journal/12478.htm" target="_blank" data-id="12478" data-field="ja"><em>Geometric and Functional Analysis</em></a> </div> <span class="Pub">Pub Date : 2025-08-06</span> <span class="Pub">DOI: 10.1134/s0026893325700220</span> </div> <div class="author" data-author="true" data-paperid="144924667">N. E. Vorobyova, Iu. V. Nikolenko, A. N. Krasnov</div> <div class="substance_2 cen" data-abstract-lang="en"> <input id="exp1_2" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_2"></label> <h3 data-test="abstract-sub-heading">Abstract</h3><p>Despite increasing data on the properties of the origins of replication, the molecular mechanisms underlying the origin recognition complex (ORC) positioning in the genome are still poorly understood. It has been suggested that the key factors determining the positioning of ORC in the genome are DNA-binding proteins that form various DNA regulatory elements, including insulators, promoters, and enhancers, thereby linking the replication program to different levels of transcriptional regulation. Previously, we demonstrated that the Su(Hw) protein is the first example of such a protein. Subsequent studies identified a number of other DNA-binding proteins, including CG10543, which may be responsible for the formation of the corresponding regulatory elements and the recruitment of transcriptional and replication complexes to their binding sites. It has been shown that the Drosophila CG10543 protein interacts with the deubiquitinating (DUB) module of the SAGA complex. The binding sites of the CG10543 protein are predominantly located in the promoter regions of active genes and colocalize with the SAGA and dSWI/SNF chromatin modification and remodeling complexes, as well as with the ORC replication complex. To investigate the role of the CG10543 protein in transcriptional regulation, an RNA-Seq experiment was conducted in Drosophila S2 cells under normal conditions and upon RNA interference with the CG10543 protein. It was shown that the CG10543 protein affects the transcription of 469 genes, with a significant portion of these genes (23%) being ecdysone-dependent genes. Ecdysone is the main steroid hormone in Drosophila, is responsible for Drosophila metamorphosis, and has a significant effect on the expression of many genes during development. We demonstrated that CG10543 sites colocalize with the CBP protein and the histone mark H3K27Ac, which are characteristic of active regulatory elements. The CG10543 protein also colocalizes with the CP190 protein, suggesting a potential mechanism of transcriptional regulation through the formation of long-range interactions between regulatory elements.</p> </div> </div> <div class="substance_2 ccn" data-abstract-lang="cn"> <input id="exp1_cn_2" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_cn_2"></label> 摘要尽管关于复制起始点特性的数据越来越多，但基因组中起始点识别复合体（ORC）定位的分子机制仍然知之甚少。研究表明，决定ORC在基因组中定位的关键因素是DNA结合蛋白，这些DNA结合蛋白形成了各种DNA调控元件，包括绝缘子、启动子和增强子，从而将复制程序与不同水平的转录调控联系起来。在此之前，我们证明了Su（Hw）蛋白是这种蛋白的第一个例子。随后的研究发现了包括CG10543在内的许多其他dna结合蛋白，它们可能负责形成相应的调控元件，并将转录和复制复合物募集到其结合位点。研究表明，果蝇CG10543蛋白与SAGA复合物的去泛素化（DUB）模块相互作用。CG10543蛋白的结合位点主要位于活性基因的启动子区域，并与SAGA和dSWI/SNF染色质修饰和重塑复合体以及ORC复制复合体共定位。为了研究CG10543蛋白在转录调控中的作用，我们在正常条件下和RNA干扰CG10543蛋白的情况下，在果蝇S2细胞中进行了RNA- seq实验。结果表明，CG10543蛋白影响469个基因的转录，其中相当一部分（23%）是蜕皮激素依赖基因。蜕皮激素是果蝇体内主要的类固醇激素，负责果蝇的变态，在发育过程中对许多基因的表达有重要影响。我们发现CG10543位点与具有活性调控元件特征的CBP蛋白和组蛋白标记H3K27Ac共定位。CG10543蛋白也与CP190蛋白共定位，提示通过调控元件之间形成远程相互作用的潜在转录调控机制。 </div> </div> <div class="wxicon"> <button class="buttonicon svgimg" onclick="logintishi(this);"> <img src="/Content/css/sci/svg/pdfl.svg" alt="求助PDF" /><em class="icontext">求助PDF</em> </button> <div style="display:none;">{"title":"CG10543 Protein Is Involved in the Regulation of Transcription of Ecdysone-Dependent Genes","authors":"N. E. Vorobyova, Iu. V. Nikolenko, A. N. Krasnov","doi":"10.1134/s0026893325700220","DOIUrl":"https://doi.org/10.1134/s0026893325700220","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Despite increasing data on the properties of the origins of replication, the molecular mechanisms underlying the origin recognition complex (ORC) positioning in the genome are still poorly understood. It has been suggested that the key factors determining the positioning of ORC in the genome are DNA-binding proteins that form various DNA regulatory elements, including insulators, promoters, and enhancers, thereby linking the replication program to different levels of transcriptional regulation. Previously, we demonstrated that the Su(Hw) protein is the first example of such a protein. Subsequent studies identified a number of other DNA-binding proteins, including CG10543, which may be responsible for the formation of the corresponding regulatory elements and the recruitment of transcriptional and replication complexes to their binding sites. It has been shown that the Drosophila CG10543 protein interacts with the deubiquitinating (DUB) module of the SAGA complex. The binding sites of the CG10543 protein are predominantly located in the promoter regions of active genes and colocalize with the SAGA and dSWI/SNF chromatin modification and remodeling complexes, as well as with the ORC replication complex. To investigate the role of the CG10543 protein in transcriptional regulation, an RNA-Seq experiment was conducted in Drosophila S2 cells under normal conditions and upon RNA interference with the CG10543 protein. It was shown that the CG10543 protein affects the transcription of 469 genes, with a significant portion of these genes (23%) being ecdysone-dependent genes. Ecdysone is the main steroid hormone in Drosophila, is responsible for Drosophila metamorphosis, and has a significant effect on the expression of many genes during development. We demonstrated that CG10543 sites colocalize with the CBP protein and the histone mark H3K27Ac, which are characteristic of active regulatory elements. The CG10543 protein also colocalizes with the CP190 protein, suggesting a potential mechanism of transcriptional regulation through the formation of long-range interactions between regulatory elements.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"30 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}</div> <span class="citeNo" data-field="citation" data-doi="10.1134/s0026893325700220">引用次数: 0</span> <button class="buttonicon" name="dangeyinyong" onclick="dangeyinyong(this);"> <img src="/Content/css/sci/svg/yy.svg" alt="引用" /> <em class="icontext">引用</em> </button> <button class="buttonicon" name="piliangyinyong" attr-id="2" attr-doi="10.1134/s0026893325700220" attr-title="CG10543 Protein Is Involved in the Regulation of Transcription of Ecdysone-Dependent Genes" attr-citationcount="0" onclick="piliangyinyong(this);"> <img src="/Content/css/sci/svg/plyy.svg" alt="批量引用" /> <em class="icontext">批量引用</em> </button> </div> </div> <div class="sslist"> <a class="caption cen" data-title-lang="en" href="/literature/144924669.htm">Local Integral Transforms and Global Spectral Decomposition</a> <a class="caption ccn" data-title-lang="cn" href="/literaturecn/144924669.htm" attr-paper="paper" attr-paperid="144924669">局部积分变换与全局谱分解</a> <div class="substance"> <span class="IF1" attr-if="if">IF 2.2 </span> <span class="fq1" attr-fq="fq">1区数学</span> <span class="qe1" attr-qe="qe">Q1 MATHEMATICS</span> <div class="journal"> <a href="/journal/12478.htm" target="_blank" data-id="12478" data-field="ja"><em>Geometric and Functional Analysis</em></a> </div> <span class="Pub">Pub Date : 2025-07-10</span> <span class="Pub">DOI: 10.1007/s00039-025-00714-0</span> </div> <div class="author" data-author="true" data-paperid="144924669">Valentin Blomer, Subhajit Jana, Paul D. Nelson</div> <div class="substance_2 cen" data-abstract-lang="en"> <input id="exp1_3" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_3"></label> <p>We establish an explicit global spectral decomposition of shifted convolution sums and the second moment of automorphic <span>(L)</span>-functions for Maaß forms with explicit integral transforms as well as explicit inversion formulae over every local field.</p> </div> </div> <div class="substance_2 ccn" data-abstract-lang="cn"> <input id="exp1_cn_3" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_cn_3"></label> 我们建立了具有显式积分变换的maasß形式的移位卷积和的显式全局谱分解和自同构(L) -函数的第二矩，以及每个局部域上的显式反演公式。 </div> </div> <div class="wxicon"> <button class="buttonicon svgimg" onclick="logintishi(this);"> <img src="/Content/css/sci/svg/pdfl.svg" alt="求助PDF" /><em class="icontext">求助PDF</em> </button> <div style="display:none;">{"title":"Local Integral Transforms and Global Spectral Decomposition","authors":"Valentin Blomer, Subhajit Jana, Paul D. Nelson","doi":"10.1007/s00039-025-00714-0","DOIUrl":"https://doi.org/10.1007/s00039-025-00714-0","url":null,"abstract":"<p>We establish an explicit global spectral decomposition of shifted convolution sums and the second moment of automorphic <span>(L)</span>-functions for Maaß forms with explicit integral transforms as well as explicit inversion formulae over every local field.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"52 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}</div> <span class="citeNo" data-field="citation" data-doi="10.1007/s00039-025-00714-0">引用次数: 0</span> <button class="buttonicon" name="dangeyinyong" onclick="dangeyinyong(this);"> <img src="/Content/css/sci/svg/yy.svg" alt="引用" /> <em class="icontext">引用</em> </button> <button class="buttonicon" name="piliangyinyong" attr-id="3" attr-doi="10.1007/s00039-025-00714-0" attr-title="Local Integral Transforms and Global Spectral Decomposition" attr-citationcount="0" onclick="piliangyinyong(this);"> <img src="/Content/css/sci/svg/plyy.svg" alt="批量引用" /> <em class="icontext">批量引用</em> </button> </div> </div> <div class="sslist"> <a class="caption cen" data-title-lang="en" href="/literature/144924670.htm">Non-vanishing of Geodesic Periods of Automorphic Forms</a> <a class="caption ccn" data-title-lang="cn" href="/literaturecn/144924670.htm" attr-paper="paper" attr-paperid="144924670">自同构形式测地线周期的不消失性</a> <div class="substance"> <span class="IF1" attr-if="if">IF 2.2 </span> <span class="fq1" attr-fq="fq">1区数学</span> <span class="qe1" attr-qe="qe">Q1 MATHEMATICS</span> <div class="journal"> <a href="/journal/12478.htm" target="_blank" data-id="12478" data-field="ja"><em>Geometric and Functional Analysis</em></a> </div> <span class="Pub">Pub Date : 2025-07-07</span> <span class="Pub">DOI: 10.1007/s00039-025-00715-z</span> </div> <div class="author" data-author="true" data-paperid="144924670">Petru Constantinescu, Asbjørn Christian Nordentoft</div> <div class="substance_2 cen" data-abstract-lang="en"> <input id="exp1_4" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_4"></label> <p>We prove that one hundred percent of the closed geodesic periods of a Hecke–Maaß cusp form for the modular group are non-vanishing when ordered by length. We present applications to the non-vanishing of central values of Rankin–Selberg <span>(L)</span>-functions. Similar results for holomorphic forms for general Fuchsian groups of finite covolume with a cusp are also obtained, as well as results towards normal distribution. Our new key ingredient is to relate the distributions of closed geodesic periods and vertical line integrals via graph theory.</p> </div> </div> <div class="substance_2 ccn" data-abstract-lang="cn"> <input id="exp1_cn_4" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_cn_4"></label> 证明了模群的hecke - maasus尖形的封闭测地周期在按长度排序时100％不消失。给出了Rankin-Selberg (L) -函数中心值不消失的应用。对于一般带尖的有限协体积的Fuchsian群的全纯形式也得到了类似的结果，并得到了正态分布的结果。我们新的关键成分是通过图论将封闭测地线周期和垂直线积分的分布联系起来。 </div> </div> <div class="wxicon"> <button class="buttonicon svgimg" onclick="logintishi(this);"> <img src="/Content/css/sci/svg/pdfl.svg" alt="求助PDF" /><em class="icontext">求助PDF</em> </button> <div style="display:none;">{"title":"Non-vanishing of Geodesic Periods of Automorphic Forms","authors":"Petru Constantinescu, Asbjørn Christian Nordentoft","doi":"10.1007/s00039-025-00715-z","DOIUrl":"https://doi.org/10.1007/s00039-025-00715-z","url":null,"abstract":"<p>We prove that one hundred percent of the closed geodesic periods of a Hecke–Maaß cusp form for the modular group are non-vanishing when ordered by length. We present applications to the non-vanishing of central values of Rankin–Selberg <span>(L)</span>-functions. Similar results for holomorphic forms for general Fuchsian groups of finite covolume with a cusp are also obtained, as well as results towards normal distribution. Our new key ingredient is to relate the distributions of closed geodesic periods and vertical line integrals via graph theory.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"38 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}</div> <span class="citeNo" data-field="citation" data-doi="10.1007/s00039-025-00715-z">引用次数: 0</span> <button class="buttonicon" name="dangeyinyong" onclick="dangeyinyong(this);"> <img src="/Content/css/sci/svg/yy.svg" alt="引用" /> <em class="icontext">引用</em> </button> <button class="buttonicon" name="piliangyinyong" attr-id="4" attr-doi="10.1007/s00039-025-00715-z" attr-title="Non-vanishing of Geodesic Periods of Automorphic Forms" attr-citationcount="0" onclick="piliangyinyong(this);"> <img src="/Content/css/sci/svg/plyy.svg" alt="批量引用" /> <em class="icontext">批量引用</em> </button> </div> </div> <div class="sslist"> <a class="caption cen" data-title-lang="en" href="/literature/144924520.htm">Prime Number Theorems for Polynomials from Homogeneous Dynamics</a> <a class="caption ccn" data-title-lang="cn" href="/literaturecn/144924520.htm" attr-paper="paper" attr-paperid="144924520">齐次动力学多项式的素数定理</a> <div class="substance"> <span class="IF1" attr-if="if">IF 2.2 </span> <span class="fq1" attr-fq="fq">1区数学</span> <span class="qe1" attr-qe="qe">Q1 MATHEMATICS</span> <div class="journal"> <a href="/journal/12478.htm" target="_blank" data-id="12478" data-field="ja"><em>Geometric and Functional Analysis</em></a> </div> <span class="Pub">Pub Date : 2025-07-07</span> <span class="Pub">DOI: 10.1007/s00039-025-00716-y</span> </div> <div class="author" data-author="true" data-paperid="144924520">Giorgos Kotsovolis, Katharine Woo</div> <div class="substance_2 cen" data-abstract-lang="en"> <input id="exp1_5" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_5"></label> <p>We establish a new class of examples of the multivariate Bateman-Horn conjecture by using tools from dynamics. These cases include the determinant polynomial on the space of <span><span style=""></span><span data-mathml='<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&#x00D7;</mo><mi>n</mi></math>' role="presentation" style="font-size: 100%; display: inline-block; position: relative;" tabindex="0"><svg aria-hidden="true" focusable="false" height="1.509ex" role="img" style="vertical-align: -0.205ex;" viewbox="0 -561.7 2423.9 649.8" width="5.63ex" xmlns:xlink="http://www.w3.org/1999/xlink"><g fill="currentColor" stroke="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use x="0" xlink:href="#MJMATHI-6E" y="0"></use><use x="822" xlink:href="#MJMAIN-D7" y="0"></use><use x="1823" xlink:href="#MJMATHI-6E" y="0"></use></g></svg><span role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>×</mo><mi>n</mi></math></span></span><script type="math/tex">ntimes n</script></span> matrices, the Pfaffian on the space of skew-symmetric <span><span style=""></span><span data-mathml='<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>n</mi><mo>&#x00D7;</mo><mn>2</mn><mi>n</mi></math>' role="presentation" style="font-size: 100%; display: inline-block; position: relative;" tabindex="0"><svg aria-hidden="true" focusable="false" height="1.909ex" role="img" style="vertical-align: -0.205ex;" viewbox="0 -733.9 3424.9 822.1" width="7.955ex" xmlns:xlink="http://www.w3.org/1999/xlink"><g fill="currentColor" stroke="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use x="0" xlink:href="#MJMAIN-32" y="0"></use><use x="500" xlink:href="#MJMATHI-6E" y="0"></use><use x="1323" xlink:href="#MJMAIN-D7" y="0"></use><use x="2323" xlink:href="#MJMAIN-32" y="0"></use><use x="2824" xlink:href="#MJMATHI-6E" y="0"></use></g></svg><span role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>n</mi><mo>×</mo><mn>2</mn><mi>n</mi></math></span></span><script type="math/tex">2ntimes 2n</script></span> matrices, and the determinant polynomial on the space of symmetric <span><span style=""></span><span data-mathml='<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&#x00D7;</mo><mi>n</mi></math>' role="presentation" style="font-size: 100%; display: inline-block; position: relative;" tabindex="0"><svg aria-hidden="true" focusable="false" height="1.512ex" role="img" style="vertical-align: -0.205ex;" viewbox="0 -562.7 2423.9 650.9" width="5.63ex" xmlns:xlink="http://www.w3.org/1999/xlink"><g fill="currentColor" stroke="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use x="0" xlink:href="#MJMATHI-6E" y="0"></use><use x="822" xlink:href="#MJMAIN-D7" y="0"></use><use x="1823" xlink: </div> </div> <div class="substance_2 ccn" data-abstract-lang="cn"> <input id="exp1_cn_5" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_cn_5"></label> 利用动力学工具建立了一类新的多元Bateman-Horn猜想的实例。这些情况包括n×nn times n个矩阵空间上的行列式多项式，偏对称2n×2n2n times 2n个矩阵空间上的Pfaffian，以及对称n×nn times n个矩阵空间上的行列式多项式。特别地，设（V，F）（V，F）是下列任意对：（Matn,det）（textrm{Mat＿n}, {}det），（Skew2n,Pff）（textrm{Skew＿2n},{}textrm{Pff}）和（Symn,det）（textrm{Sym＿n}, {}det）。然后，我们得到了πV，F(T)=＃{v∈v:max(|vi|)≤T，F(v)是质数}，pi ＿V，F{(T)= ＃｛v }in v: max (|{v＿i}|) leq T，F(v) text{ is prime}｝的渐近，符合batemanan - horn预测。我们的证明的关键成分是由Linnik等分布给出的FF水平集上的积分点的渐近计数，由锥体给出的盒子的几何近似，以及一个上界筛来限制近似错过的素数值的数量。在对称矩阵上的行列式多项式的情况下，我们还必须使用西格尔质量公式来计算主项的局部密度积。 </div> </div> <div class="wxicon"> <button class="buttonicon svgimg" onclick="logintishi(this);"> <img src="/Content/css/sci/svg/pdfl.svg" alt="求助PDF" /><em class="icontext">求助PDF</em> </button> <div style="display:none;">{"title":"Prime Number Theorems for Polynomials from Homogeneous Dynamics","authors":"Giorgos Kotsovolis, Katharine Woo","doi":"10.1007/s00039-025-00716-y","DOIUrl":"https://doi.org/10.1007/s00039-025-00716-y","url":null,"abstract":"&lt;p&gt;We establish a new class of examples of the multivariate Bateman-Horn conjecture by using tools from dynamics. These cases include the determinant polynomial on the space of &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"1.509ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -561.7 2423.9 649.8\" width=\"5.63ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-6E\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"822\" xlink:href=\"#MJMAIN-D7\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1823\" xlink:href=\"#MJMATHI-6E\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span role=\"presentation\"&gt;&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;ntimes n&lt;/script&gt;&lt;/span&gt; matrices, the Pfaffian on the space of skew-symmetric &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"1.909ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -733.9 3424.9 822.1\" width=\"7.955ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMAIN-32\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"500\" xlink:href=\"#MJMATHI-6E\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1323\" xlink:href=\"#MJMAIN-D7\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"2323\" xlink:href=\"#MJMAIN-32\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"2824\" xlink:href=\"#MJMATHI-6E\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span role=\"presentation\"&gt;&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;2ntimes 2n&lt;/script&gt;&lt;/span&gt; matrices, and the determinant polynomial on the space of symmetric &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"1.512ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -562.7 2423.9 650.9\" width=\"5.63ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-6E\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"822\" xlink:href=\"#MJMAIN-D7\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1823\" xlink:","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"31 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}</div> <span class="citeNo" data-field="citation" data-doi="10.1007/s00039-025-00716-y">引用次数: 0</span> <button class="buttonicon" name="dangeyinyong" onclick="dangeyinyong(this);"> <img src="/Content/css/sci/svg/yy.svg" alt="引用" /> <em class="icontext">引用</em> </button> <button class="buttonicon" name="piliangyinyong" attr-id="5" attr-doi="10.1007/s00039-025-00716-y" attr-title="Prime Number Theorems for Polynomials from Homogeneous Dynamics" attr-citationcount="0" onclick="piliangyinyong(this);"> <img src="/Content/css/sci/svg/plyy.svg" alt="批量引用" /> <em class="icontext">批量引用</em> </button> </div> </div> <div class="sslist"> <a class="caption cen" data-title-lang="en" href="/literature/144924672.htm">Homomorphisms to 3–Manifold Groups</a> <a class="caption ccn" data-title-lang="cn" href="/literaturecn/144924672.htm" attr-paper="paper" attr-paperid="144924672">3流形群的同态</a> <div class="substance"> <span class="IF1" attr-if="if">IF 2.2 </span> <span class="fq1" attr-fq="fq">1区数学</span> <span class="qe1" attr-qe="qe">Q1 MATHEMATICS</span> <div class="journal"> <a href="/journal/12478.htm" target="_blank" data-id="12478" data-field="ja"><em>Geometric and Functional Analysis</em></a> </div> <span class="Pub">Pub Date : 2025-05-28</span> <span class="Pub">DOI: 10.1007/s00039-025-00713-1</span> </div> <div class="author" data-author="true" data-paperid="144924672">Daniel Groves, Michael Hull, Hao Liang</div> <div class="substance_2 cen" data-abstract-lang="en"> <input id="exp1_6" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_6"></label> <p>We prove foundational results about the set of homomorphisms from a finitely generated group to the collection of all fundamental groups of compact 3–manifolds and answer questions of Agol–Liu (J. Am. Math. Soc. 25(1):151–187, 2012) and Reid–Wang–Zhou (Acta Math. Sin. Engl. Ser. 18(1):157–172, 2002).</p> </div> </div> <div class="substance_2 ccn" data-abstract-lang="cn"> <input id="exp1_cn_6" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_cn_6"></label> 证明了紧3流形从有限生成群到所有基本群集合的同态集的基本结果，并回答了Agol-Liu （J. Am.）的问题。数学。数学学报，25(1):151-187,2012)。罪。心血管病。学报，18(1):157-172,2002)。 </div> </div> <div class="wxicon"> <button class="buttonicon svgimg" onclick="logintishi(this);"> <img src="/Content/css/sci/svg/pdfl.svg" alt="求助PDF" /><em class="icontext">求助PDF</em> </button> <div style="display:none;">{"title":"Homomorphisms to 3–Manifold Groups","authors":"Daniel Groves, Michael Hull, Hao Liang","doi":"10.1007/s00039-025-00713-1","DOIUrl":"https://doi.org/10.1007/s00039-025-00713-1","url":null,"abstract":"<p>We prove foundational results about the set of homomorphisms from a finitely generated group to the collection of all fundamental groups of compact 3–manifolds and answer questions of Agol–Liu (J. Am. Math. Soc. 25(1):151–187, 2012) and Reid–Wang–Zhou (Acta Math. Sin. Engl. Ser. 18(1):157–172, 2002).</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"25 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}</div> <span class="citeNo" data-field="citation" data-doi="10.1007/s00039-025-00713-1">引用次数: 0</span> <button class="buttonicon" name="dangeyinyong" onclick="dangeyinyong(this);"> <img src="/Content/css/sci/svg/yy.svg" alt="引用" /> <em class="icontext">引用</em> </button> <button class="buttonicon" name="piliangyinyong" attr-id="6" attr-doi="10.1007/s00039-025-00713-1" attr-title="Homomorphisms to 3–Manifold Groups" attr-citationcount="0" onclick="piliangyinyong(this);"> <img src="/Content/css/sci/svg/plyy.svg" alt="批量引用" /> <em class="icontext">批量引用</em> </button> </div> </div> <div class="sslist"> <a class="caption cen" data-title-lang="en" href="/literature/144924671.htm">Locally Homogeneous Axiom A Flows I: Projective Anosov Subgroups and Exponential Mixing</a> <a class="caption ccn" data-title-lang="cn" href="/literaturecn/144924671.htm" attr-paper="paper" attr-paperid="144924671">局部齐次公理A流I：投影Anosov子群与指数混合</a> <div class="substance"> <span class="IF1" attr-if="if">IF 2.2 </span> <span class="fq1" attr-fq="fq">1区数学</span> <span class="qe1" attr-qe="qe">Q1 MATHEMATICS</span> <div class="journal"> <a href="/journal/12478.htm" target="_blank" data-id="12478" data-field="ja"><em>Geometric and Functional Analysis</em></a> </div> <span class="Pub">Pub Date : 2025-05-28</span> <span class="Pub">DOI: 10.1007/s00039-025-00712-2</span> </div> <div class="author" data-author="true" data-paperid="144924671">Benjamin Delarue, Daniel Monclair, Andrew Sanders</div> <div class="substance_2 cen" data-abstract-lang="en"> <input id="exp1_7" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_7"></label> <p>By constructing a non-empty domain of discontinuity in a suitable homogeneous space, we prove that every torsion-free projective Anosov subgroup is the monodromy group of a locally homogeneous contact Axiom A dynamical system with a unique basic hyperbolic set on which the flow is conjugate to the refraction flow of Sambarino. Under the assumption of irreducibility, we utilize the work of Stoyanov to establish spectral estimates for the associated complex Ruelle transfer operators, and by way of corollary: exponential mixing, exponentially decaying error term in the prime orbit theorem, and a spectral gap for the Ruelle zeta function. With no irreducibility assumption, results of Dyatlov-Guillarmou imply the global meromorphic continuation of zeta functions with smooth weights, as well as the existence of a discrete spectrum of Ruelle-Pollicott resonances and (co)-resonant states. We apply our results to space-like geodesic flows for the convex cocompact pseudo-Riemannian manifolds of Danciger-Guéritaud-Kassel, and the Benoist-Hilbert geodesic flow for strictly convex real projective manifolds.</p> </div> </div> <div class="substance_2 ccn" data-abstract-lang="cn"> <input id="exp1_cn_7" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_cn_7"></label> 通过在合适的齐次空间中构造一个非空的不连续域，证明了具有唯一基本双曲集的局部齐次接触公理a动力系统的无扭转投影Anosov子群是其单群，且该系统上的流动共轭于Sambarino折射流。在不可约的假设下，我们利用Stoyanov的工作建立了相关复Ruelle传递算子的谱估计，并通过推论：指数混合、素轨道定理中的指数衰减误差项和Ruelle zeta函数的谱间隙。在没有不可约假设的情况下，Dyatlov-Guillarmou的结果暗示了具有光滑权值的zeta函数的全局亚纯延后，以及Ruelle-Pollicott共振和(co)-共振态的离散谱的存在。我们将我们的结果应用于danciger - gu<s:1>里多-卡塞尔的凸紧伪黎曼流形的类空间测地线流，以及严格凸实射影流形的Benoist-Hilbert测地线流。 </div> </div> <div class="wxicon"> <button class="buttonicon svgimg" onclick="logintishi(this);"> <img src="/Content/css/sci/svg/pdfl.svg" alt="求助PDF" /><em class="icontext">求助PDF</em> </button> <div style="display:none;">{"title":"Locally Homogeneous Axiom A Flows I: Projective Anosov Subgroups and Exponential Mixing","authors":"Benjamin Delarue, Daniel Monclair, Andrew Sanders","doi":"10.1007/s00039-025-00712-2","DOIUrl":"https://doi.org/10.1007/s00039-025-00712-2","url":null,"abstract":"<p>By constructing a non-empty domain of discontinuity in a suitable homogeneous space, we prove that every torsion-free projective Anosov subgroup is the monodromy group of a locally homogeneous contact Axiom A dynamical system with a unique basic hyperbolic set on which the flow is conjugate to the refraction flow of Sambarino. Under the assumption of irreducibility, we utilize the work of Stoyanov to establish spectral estimates for the associated complex Ruelle transfer operators, and by way of corollary: exponential mixing, exponentially decaying error term in the prime orbit theorem, and a spectral gap for the Ruelle zeta function. With no irreducibility assumption, results of Dyatlov-Guillarmou imply the global meromorphic continuation of zeta functions with smooth weights, as well as the existence of a discrete spectrum of Ruelle-Pollicott resonances and (co)-resonant states. We apply our results to space-like geodesic flows for the convex cocompact pseudo-Riemannian manifolds of Danciger-Guéritaud-Kassel, and the Benoist-Hilbert geodesic flow for strictly convex real projective manifolds.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"23 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}</div> <span class="citeNo" data-field="citation" data-doi="10.1007/s00039-025-00712-2">引用次数: 0</span> <button class="buttonicon" name="dangeyinyong" onclick="dangeyinyong(this);"> <img src="/Content/css/sci/svg/yy.svg" alt="引用" /> <em class="icontext">引用</em> </button> <button class="buttonicon" name="piliangyinyong" attr-id="7" attr-doi="10.1007/s00039-025-00712-2" attr-title="Locally Homogeneous Axiom A Flows I: Projective Anosov Subgroups and Exponential Mixing" attr-citationcount="0" onclick="piliangyinyong(this);"> <img src="/Content/css/sci/svg/plyy.svg" alt="批量引用" /> <em class="icontext">批量引用</em> </button> </div> </div> <div class="sslist"> <a class="caption cen" data-title-lang="en" href="/literature/143945583.htm">Entropy and Stability of Hyperbolic Manifolds</a> <a class="caption ccn" data-title-lang="cn" href="/literaturecn/143945583.htm" attr-paper="paper" attr-paperid="143945583">双曲流形的熵与稳定性</a> <div class="substance"> <span class="IF1" attr-if="if">IF 2.2 </span> <span class="fq1" attr-fq="fq">1区数学</span> <span class="qe1" attr-qe="qe">Q1 MATHEMATICS</span> <div class="journal"> <a href="/journal/12478.htm" target="_blank" data-id="12478" data-field="ja"><em>Geometric and Functional Analysis</em></a> </div> <span class="Pub">Pub Date : 2025-05-14</span> <span class="Pub">DOI: 10.1007/s00039-025-00711-3</span> </div> <div class="author" data-author="true" data-paperid="143945583">Antoine Song</div> <div class="substance_2 cen" data-abstract-lang="en"> <input id="exp1_8" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_8"></label> <p>Let (<i>M</i>,<i>g</i><sub>0</sub>) be a closed oriented hyperbolic manifold of dimension at least 3. By the volume entropy inequality of G. Besson, G. Courtois and S. Gallot, for any Riemannian metric <i>g</i> on <i>M</i> with same volume as <i>g</i><sub>0</sub>, its volume entropy <i>h</i>(<i>g</i>) satisfies <i>h</i>(<i>g</i>)≥<i>n</i>−1 with equality only when <i>g</i> is isometric to <i>g</i><sub>0</sub>. We show that the hyperbolic metric <i>g</i><sub>0</sub> is stable in the following sense: if <i>g</i><sub><i>i</i></sub> is a sequence of Riemaniann metrics on <i>M</i> of same volume as <i>g</i><sub>0</sub> and if <i>h</i>(<i>g</i><sub><i>i</i></sub>) converges to <i>n</i>−1, then there are smooth subsets <i>Z</i><sub><i>i</i></sub>⊂<i>M</i> such that both <span>(operatorname{Vol}(Z_{i},g_{i}))</span> and <span>(operatorname{Area}(partial Z_{i},g_{i}))</span> tend to 0, and (<i>M</i>∖<i>Z</i><sub><i>i</i></sub>,<i>g</i><sub><i>i</i></sub>) converges to (<i>M</i>,<i>g</i><sub>0</sub>) in the measured Gromov-Hausdorff topology. The proof relies on showing that any spherical Plateau solution for <i>M</i> is intrinsically isomorphic to <span>((M,frac{(n-1)^{2}}{4n} g_{0}))</span>.</p> </div> </div> <div class="substance_2 ccn" data-abstract-lang="cn"> <input id="exp1_cn_8" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_cn_8"></label> 设（M,g0）是一个至少维数为3的封闭定向双曲流形。由g . Besson, g . Courtois和S. Gallot的体积熵不等式可知，对于M上体积与g0相等的黎曼度规g，其体积熵h(g)仅在g与g0等距时满足h(g)≥n−1且相等。我们证明了双曲度规g0在以下意义上是稳定的：如果gi是与g0体积相同的M上的黎曼度量序列，并且如果h（gi）收敛于n−1，则存在光滑子集Zi∧M，使得(operatorname{Vol}(Z_{i},g_{i}))和(operatorname{Area}(partial Z_{i},g_{i}))都趋于0，并且（M∈Zi,gi）在测量的Gromov-Hausdorff拓扑中收敛于（M,g0）。证明依赖于证明M的任何球面平台解本质上同构于((M,frac{(n-1)^{2}}{4n} g_{0}))。 </div> </div> <div class="wxicon"> <button class="buttonicon svgimg" onclick="logintishi(this);"> <img src="/Content/css/sci/svg/pdfl.svg" alt="求助PDF" /><em class="icontext">求助PDF</em> </button> <div style="display:none;">{"title":"Entropy and Stability of Hyperbolic Manifolds","authors":"Antoine Song","doi":"10.1007/s00039-025-00711-3","DOIUrl":"https://doi.org/10.1007/s00039-025-00711-3","url":null,"abstract":"<p>Let (<i>M</i>,<i>g</i><sub>0</sub>) be a closed oriented hyperbolic manifold of dimension at least 3. By the volume entropy inequality of G. Besson, G. Courtois and S. Gallot, for any Riemannian metric <i>g</i> on <i>M</i> with same volume as <i>g</i><sub>0</sub>, its volume entropy <i>h</i>(<i>g</i>) satisfies <i>h</i>(<i>g</i>)≥<i>n</i>−1 with equality only when <i>g</i> is isometric to <i>g</i><sub>0</sub>. We show that the hyperbolic metric <i>g</i><sub>0</sub> is stable in the following sense: if <i>g</i><sub><i>i</i></sub> is a sequence of Riemaniann metrics on <i>M</i> of same volume as <i>g</i><sub>0</sub> and if <i>h</i>(<i>g</i><sub><i>i</i></sub>) converges to <i>n</i>−1, then there are smooth subsets <i>Z</i><sub><i>i</i></sub>⊂<i>M</i> such that both <span>(operatorname{Vol}(Z_{i},g_{i}))</span> and <span>(operatorname{Area}(partial Z_{i},g_{i}))</span> tend to 0, and (<i>M</i>∖<i>Z</i><sub><i>i</i></sub>,<i>g</i><sub><i>i</i></sub>) converges to (<i>M</i>,<i>g</i><sub>0</sub>) in the measured Gromov-Hausdorff topology. The proof relies on showing that any spherical Plateau solution for <i>M</i> is intrinsically isomorphic to <span>((M,frac{(n-1)^{2}}{4n} g_{0}))</span>.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"29 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143945583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}</div> <span class="citeNo" data-field="citation" data-doi="10.1007/s00039-025-00711-3">引用次数: 0</span> <button class="buttonicon" name="dangeyinyong" onclick="dangeyinyong(this);"> <img src="/Content/css/sci/svg/yy.svg" alt="引用" /> <em class="icontext">引用</em> </button> <button class="buttonicon" name="piliangyinyong" attr-id="8" attr-doi="10.1007/s00039-025-00711-3" attr-title="Entropy and Stability of Hyperbolic Manifolds" attr-citationcount="0" onclick="piliangyinyong(this);"> <img src="/Content/css/sci/svg/plyy.svg" alt="批量引用" /> <em class="icontext">批量引用</em> </button> </div> </div> <div class="sslist"> <a class="caption cen" data-title-lang="en" href="/literature/143915961.htm">Rate Distortion Dimension of Random Brody Curves</a> <a class="caption ccn" data-title-lang="cn" href="/literaturecn/143915961.htm" attr-paper="paper" attr-paperid="143915961">随机Brody曲线的速率畸变维数</a> <div class="substance"> <span class="IF1" attr-if="if">IF 2.2 </span> <span class="fq1" attr-fq="fq">1区数学</span> <span class="qe1" attr-qe="qe">Q1 MATHEMATICS</span> <div class="journal"> <a href="/journal/12478.htm" target="_blank" data-id="12478" data-field="ja"><em>Geometric and Functional Analysis</em></a> </div> <span class="Pub">Pub Date : 2025-05-07</span> <span class="Pub">DOI: 10.1007/s00039-025-00709-x</span> </div> <div class="author" data-author="true" data-paperid="143915961">Masaki Tsukamoto</div> <div class="substance_2 cen" data-abstract-lang="en"> <input id="exp1_9" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_9"></label> <p>The main purpose of this paper is to propose an ergodic theoretic approach to the study of entire holomorphic curves. Brody curves are one-Lipschitz holomorphic maps from the complex plane to the complex projective space. They admit a natural group action, and “random Brody curves” in the title refers to invariant probability measures for it. We study their geometric and dynamical properties. Given an invariant probability measure <i>μ</i> on the space of Brody curves, our first main theorem claims that its rate distortion dimension is bounded by the integral of a “geometric potential” over <i>μ</i>. This result is analogous to the Ruelle inequality of smooth ergodic theory. Our second main theorem claims that there exists a rich variety of invariant probability measures attaining equality in this “Ruelle inequality for Brody curves”. The main tools of the proofs are the deformation theory of Brody curves and the variational principle for mean dimension with potential. This approach is motivated by the theory of thermodynamic formalism for Axiom A diffeomorphisms.</p> </div> </div> <div class="substance_2 ccn" data-abstract-lang="cn"> <input id="exp1_cn_9" class="exp" type="checkbox"> <div class="text"> <label class="Bon" for="exp1_cn_9"></label> 本文的主要目的是提出一种遍历的理论方法来研究全纯曲线。Brody曲线是从复平面到复射影空间的单lipschitz全纯映射。他们承认自然的群体行为，标题中的“随机布罗迪曲线”指的是它的不变概率度量。我们研究了它们的几何和动力学性质。给定Brody曲线空间上的一个不变概率测度μ，我们的第一个主要定理表明它的率畸变维由“几何势”在μ上的积分限定。这一结果与光滑遍历理论中的Ruelle不等式类似。我们的第二个主要定理表明，在这个“Brody曲线的Ruelle不等式”中存在着丰富多样的相等不变概率测度。证明的主要工具是Brody曲线的变形理论和带势的平均维数的变分原理。这种方法的动机是热力学形式论的公理A微分同态。 </div> </div> <div class="wxicon"> <button class="buttonicon svgimg" onclick="logintishi(this);"> <img src="/Content/css/sci/svg/pdfl.svg" alt="求助PDF" /><em class="icontext">求助PDF</em> </button> <div style="display:none;">{"title":"Rate Distortion Dimension of Random Brody Curves","authors":"Masaki Tsukamoto","doi":"10.1007/s00039-025-00709-x","DOIUrl":"https://doi.org/10.1007/s00039-025-00709-x","url":null,"abstract":"<p>The main purpose of this paper is to propose an ergodic theoretic approach to the study of entire holomorphic curves. Brody curves are one-Lipschitz holomorphic maps from the complex plane to the complex projective space. They admit a natural group action, and “random Brody curves” in the title refers to invariant probability measures for it. We study their geometric and dynamical properties. Given an invariant probability measure <i>μ</i> on the space of Brody curves, our first main theorem claims that its rate distortion dimension is bounded by the integral of a “geometric potential” over <i>μ</i>. This result is analogous to the Ruelle inequality of smooth ergodic theory. Our second main theorem claims that there exists a rich variety of invariant probability measures attaining equality in this “Ruelle inequality for Brody curves”. The main tools of the proofs are the deformation theory of Brody curves and the variational principle for mean dimension with potential. This approach is motivated by the theory of thermodynamic formalism for Axiom A diffeomorphisms.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"17 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143915961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}</div> <span class="citeNo" data-field="citation" data-doi="10.1007/s00039-025-00709-x">引用次数: 0</span> <button class="buttonicon" name="dangeyinyong" onclick="dangeyinyong(this);"> <img src="/Content/css/sci/svg/yy.svg" alt="引用" /> <em class="icontext">引用</em> </button> <button class="buttonicon" name="piliangyinyong" attr-id="9" attr-doi="10.1007/s00039-025-00709-x" attr-title="Rate Distortion Dimension of Random Brody Curves" attr-citationcount="0" onclick="piliangyinyong(this);"> <img src="/Content/css/sci/svg/plyy.svg" alt="批量引用" /> <em class="icontext">批量引用</em> </button> </div> </div> <div class="pageBox"> <div class="page"> <a href="/literature_d12478.htm" data-page-number="1">首页</a> <a href="/literature_d12478.htm" data-page-number="1">上一页</a> <ul> <li><a href="/literature_d12478.htm" data-page-number="1">1</a></li> <li class="CC round3"><a href="/literature_d12478_2.htm" data-page-number="2">2</a></li> <li><a href="/literature_d12478_3.htm" data-page-number="3">3</a></li> <li><a href="/literature_d12478_4.htm" data-page-number="4">4</a></li> <li><a href="/literature_d12478_5.htm" data-page-number="5">5</a></li> <li><a href="/literature_d12478_6.htm" data-page-number="6">6</a></li> <li><a href="/literature_d12478_7.htm" data-page-number="7">7</a></li> <li><a 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