Pub Date : 2020-01-01DOI: 10.1007/978-3-030-53725-8_2
F. C. Marques, A. Neves
{"title":"Applications of Min–Max Methods to Geometry","authors":"F. C. Marques, A. Neves","doi":"10.1007/978-3-030-53725-8_2","DOIUrl":"https://doi.org/10.1007/978-3-030-53725-8_2","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"245 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73188941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.1007/978-3-030-53725-8_4
Paul Yang
{"title":"Pseudo-Hermitian Geometry in 3D","authors":"Paul Yang","doi":"10.1007/978-3-030-53725-8_4","DOIUrl":"https://doi.org/10.1007/978-3-030-53725-8_4","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"111 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80685667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01Epub Date: 2019-04-18DOI: 10.1007/s12220-019-00191-6
Stefan Fürdös
In this article, the notion of ultradifferentiable CR manifold is introduced and an ultradifferentiable regularity result for finitely nondegenerate CR mappings is proven. Here, ultradifferentiable means with respect to Denjoy-Carleman classes defined by weight sequences. Furthermore, the regularity of infinitesimal CR automorphisms on ultradifferentiable abstract CR manifolds is investigated.
{"title":"Ultradifferentiable CR Manifolds.","authors":"Stefan Fürdös","doi":"10.1007/s12220-019-00191-6","DOIUrl":"https://doi.org/10.1007/s12220-019-00191-6","url":null,"abstract":"<p><p>In this article, the notion of ultradifferentiable CR manifold is introduced and an ultradifferentiable regularity result for finitely nondegenerate CR mappings is proven. Here, ultradifferentiable means with respect to Denjoy-Carleman classes defined by weight sequences. Furthermore, the regularity of infinitesimal CR automorphisms on ultradifferentiable abstract CR manifolds is investigated.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"30 3","pages":"3064-3098"},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-019-00191-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38118322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01Epub Date: 2019-05-10DOI: 10.1007/s12220-019-00203-5
Javier Jiménez-Garrido, Javier Sanz, Gerhard Schindl
We prove that, for asymptotically bounded holomorphic functions in a sector in an asymptotic expansion in a single direction towards the vertex with constraints in terms of a logarithmically convex sequence admitting a nonzero proximate order entails asymptotic expansion in the whole sector with control in terms of the same sequence. This generalizes a result by Fruchard and Zhang for Gevrey asymptotic expansions, and the proof strongly rests on a suitably refined version of the classical Phragmén-Lindelöf theorem, here obtained for functions whose growth in a sector is specified by a nonzero proximate order in the sense of Lindelöf and Valiron.
{"title":"A Phragmén-Lindelöf Theorem via Proximate Orders, and the Propagation of Asymptotics.","authors":"Javier Jiménez-Garrido, Javier Sanz, Gerhard Schindl","doi":"10.1007/s12220-019-00203-5","DOIUrl":"https://doi.org/10.1007/s12220-019-00203-5","url":null,"abstract":"<p><p>We prove that, for asymptotically bounded holomorphic functions in a sector in <math><mrow><mi>C</mi> <mo>,</mo></mrow> </math> an asymptotic expansion in a single direction towards the vertex with constraints in terms of a logarithmically convex sequence admitting a nonzero proximate order entails asymptotic expansion in the whole sector with control in terms of the same sequence. This generalizes a result by Fruchard and Zhang for Gevrey asymptotic expansions, and the proof strongly rests on a suitably refined version of the classical Phragmén-Lindelöf theorem, here obtained for functions whose growth in a sector is specified by a nonzero proximate order in the sense of Lindelöf and Valiron.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"30 4","pages":"3458-3483"},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-019-00203-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38553057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-09DOI: 10.1007/s12220-020-00388-0
M. Pramanik, A. Seeger
{"title":"$${mathbf {L}}^{{mathbf {p}}}$$-Sobolev Estimates for a Class of Integral Operators with Folding Canonical Relations","authors":"M. Pramanik, A. Seeger","doi":"10.1007/s12220-020-00388-0","DOIUrl":"https://doi.org/10.1007/s12220-020-00388-0","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"1 1","pages":"1-41"},"PeriodicalIF":1.1,"publicationDate":"2019-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-020-00388-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47311598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-11DOI: 10.1007/978-3-030-34953-0_11
Yanyan Li, Luc Nguyen, Bo Wang
{"title":"Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry","authors":"Yanyan Li, Luc Nguyen, Bo Wang","doi":"10.1007/978-3-030-34953-0_11","DOIUrl":"https://doi.org/10.1007/978-3-030-34953-0_11","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"144 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74025078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01Epub Date: 2018-01-25DOI: 10.1007/s12220-018-9985-6
Xueyuan Wan
In this paper, we get an inequality in terms of holomorphic sectional curvature of complex Finsler metrics. As applications, we prove a Schwarz Lemma from a complete Riemannian manifold to a complex Finsler manifold. We also show that a strongly pseudoconvex complex Finsler manifold with semi-positive but not identically zero holomorphic sectional curvature has negative Kodaira dimension under an extra condition.
{"title":"Holomorphic Sectional Curvature of Complex Finsler Manifolds.","authors":"Xueyuan Wan","doi":"10.1007/s12220-018-9985-6","DOIUrl":"https://doi.org/10.1007/s12220-018-9985-6","url":null,"abstract":"<p><p>In this paper, we get an inequality in terms of holomorphic sectional curvature of complex Finsler metrics. As applications, we prove a Schwarz Lemma from a complete Riemannian manifold to a complex Finsler manifold. We also show that a strongly pseudoconvex complex Finsler manifold with semi-positive but not identically zero holomorphic sectional curvature has negative Kodaira dimension under an extra condition.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"29 1","pages":"194-216"},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-018-9985-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36945698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01Epub Date: 2018-02-06DOI: 10.1007/s12220-018-9989-2
Dorothee Frey, Zoe Nieraeth
We consider operators T satisfying a sparse domination property with averaging exponents . We prove weighted strong type boundedness for and use new techniques to prove weighted weak type boundedness with quantitative mixed - estimates, generalizing results of Lerner, Ombrosi, and Pérez and Hytönen and Pérez. Even in the case we improve upon their results as we do not make use of a Hörmander condition of the operator T. Moreover, we also establish a dual weak type estimate. In a last part, we give a result on the optimality of the weighted strong type bounds including those previously obtained by Bernicot, Frey, and Petermichl.
我们考虑算子T满足一个稀疏支配性质|⟨T f, g⟩|≤c∑Q∈S⟨f⟩p 0, Q⟨g⟩Q 0 '， Q | Q |平均指数1≤p 0 Q 0≤∞。我们证明了p 0 p q 0的加权强型有界性，并利用新技术用定量混合a1 - A∞估计证明了加权弱型(p 0, p 0)有界性，推广了Lerner, Ombrosi, and p兼并和Hytönen and p兼并的结果。即使在p 0 = 1的情况下，我们也改进了他们的结果，因为我们没有利用算子t的Hörmander条件。此外，我们还建立了一个对偶弱类型(q0 '， q0 ')估计。在最后一部分中，我们给出了加权强类型界的最优性的结果，包括以前由Bernicot, Frey和Petermichl得到的结果。
{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">Weak and Strong Type <ns0:math><ns0:msub><ns0:mi>A</ns0:mi> <ns0:mn>1</ns0:mn></ns0:msub> </ns0:math> - <ns0:math><ns0:msub><ns0:mi>A</ns0:mi> <ns0:mi>∞</ns0:mi></ns0:msub> </ns0:math> Estimates for Sparsely Dominated Operators.","authors":"Dorothee Frey, Zoe Nieraeth","doi":"10.1007/s12220-018-9989-2","DOIUrl":"https://doi.org/10.1007/s12220-018-9989-2","url":null,"abstract":"<p><p>We consider operators <i>T</i> satisfying a sparse domination property <dispformula> <math> <mrow> <mtable> <mtr> <mtd> <mrow><mrow><mo>|</mo> <mrow><mo>⟨</mo> <mi>T</mi> <mi>f</mi> <mo>,</mo> <mi>g</mi> <mo>⟩</mo></mrow> <mo>|</mo></mrow> <mo>≤</mo> <mi>c</mi> <munder><mo>∑</mo> <mrow><mi>Q</mi> <mo>∈</mo> <mi>S</mi></mrow> </munder> <msub><mrow><mo>⟨</mo> <mi>f</mi> <mo>⟩</mo></mrow> <mrow><msub><mi>p</mi> <mn>0</mn></msub> <mo>,</mo> <mi>Q</mi></mrow> </msub> <msub><mrow><mo>⟨</mo> <mi>g</mi> <mo>⟩</mo></mrow> <mrow><msubsup><mi>q</mi> <mn>0</mn> <mo>'</mo></msubsup> <mo>,</mo> <mi>Q</mi></mrow> </msub> <mrow><mo>|</mo> <mi>Q</mi> <mo>|</mo></mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </math> </dispformula> with averaging exponents <math><mrow><mn>1</mn> <mo>≤</mo> <msub><mi>p</mi> <mn>0</mn></msub> <mo><</mo> <msub><mi>q</mi> <mn>0</mn></msub> <mo>≤</mo> <mi>∞</mi></mrow> </math> . We prove weighted strong type boundedness for <math> <mrow><msub><mi>p</mi> <mn>0</mn></msub> <mo><</mo> <mi>p</mi> <mo><</mo> <msub><mi>q</mi> <mn>0</mn></msub> </mrow> </math> and use new techniques to prove weighted weak type <math><mrow><mo>(</mo> <msub><mi>p</mi> <mn>0</mn></msub> <mo>,</mo> <msub><mi>p</mi> <mn>0</mn></msub> <mo>)</mo></mrow> </math> boundedness with quantitative mixed <math><msub><mi>A</mi> <mn>1</mn></msub> </math> - <math><msub><mi>A</mi> <mi>∞</mi></msub> </math> estimates, generalizing results of Lerner, Ombrosi, and Pérez and Hytönen and Pérez. Even in the case <math> <mrow><msub><mi>p</mi> <mn>0</mn></msub> <mo>=</mo> <mn>1</mn></mrow> </math> we improve upon their results as we do not make use of a Hörmander condition of the operator <i>T</i>. Moreover, we also establish a dual weak type <math><mrow><mo>(</mo> <msubsup><mi>q</mi> <mn>0</mn> <mo>'</mo></msubsup> <mo>,</mo> <msubsup><mi>q</mi> <mn>0</mn> <mo>'</mo></msubsup> <mo>)</mo></mrow> </math> estimate. In a last part, we give a result on the optimality of the weighted strong type bounds including those previously obtained by Bernicot, Frey, and Petermichl.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"29 1","pages":"247-282"},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-018-9989-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36945699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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