Pub Date : 2023-01-24DOI: 10.1007/s00039-023-00628-9
Hiroyasu Izeki
Let $Gamma$ be a finitely generated group equipped with a symmetric and nondegenerate probability measure $mu$ with finite second moment, and $Y$ a CAT(0) space which is either proper or of finite telescopic dimension. We show that if an isometric action of $Gamma$ on $Y$ has vanishing rate of escape with respect to $mu$ and does not fix a point in the boundary at infinity of $Y$, then there exists a flat subspace in $Y$ which is left invariant under the action of $Gamma$. In the proof of this result, an equivariant $mu$-harmonic map from $Gamma$ into $Y$ plays an important role.
{"title":"Isometric group actions with vanishing rate of escape on $$textrm{CAT}(0)$$ spaces","authors":"Hiroyasu Izeki","doi":"10.1007/s00039-023-00628-9","DOIUrl":"https://doi.org/10.1007/s00039-023-00628-9","url":null,"abstract":"Let $Gamma$ be a finitely generated group equipped with a symmetric and nondegenerate probability measure $mu$ with finite second moment, and $Y$ a CAT(0) space which is either proper or of finite telescopic dimension. We show that if an isometric action of $Gamma$ on $Y$ has vanishing rate of escape with respect to $mu$ and does not fix a point in the boundary at infinity of $Y$, then there exists a flat subspace in $Y$ which is left invariant under the action of $Gamma$. In the proof of this result, an equivariant $mu$-harmonic map from $Gamma$ into $Y$ plays an important role.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136198725","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}
Pub Date : 2023-01-02DOI: 10.1007/s00039-023-00646-7
O. Solan, Y. Yifrach
{"title":"Tori Approximation of Families of Diagonally Invariant Measures","authors":"O. Solan, Y. Yifrach","doi":"10.1007/s00039-023-00646-7","DOIUrl":"https://doi.org/10.1007/s00039-023-00646-7","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"33 1","pages":"1354 - 1378"},"PeriodicalIF":2.2,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47938375","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}
Pub Date : 2022-11-29DOI: 10.1007/s00039-022-00622-7
Yuanqing Cai, S. Friedberg, Eyal Kaplan
{"title":"Publisher Correction to: The generalized doubling method: local theory","authors":"Yuanqing Cai, S. Friedberg, Eyal Kaplan","doi":"10.1007/s00039-022-00622-7","DOIUrl":"https://doi.org/10.1007/s00039-022-00622-7","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"32 1","pages":"1334 - 1334"},"PeriodicalIF":2.2,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46602211","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}
Pub Date : 2022-11-03DOI: 10.1007/s00039-023-00632-z
A. Avila, D. Damanik, A. Gorodetski
{"title":"The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials","authors":"A. Avila, D. Damanik, A. Gorodetski","doi":"10.1007/s00039-023-00632-z","DOIUrl":"https://doi.org/10.1007/s00039-023-00632-z","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"33 1","pages":"364-375"},"PeriodicalIF":2.2,"publicationDate":"2022-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51866871","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}
Pub Date : 2022-10-22DOI: 10.1007/s00039-022-00620-9
Wangjian Jian, Jian Song
{"title":"Diameter estimates for long-time solutions of the Kähler–Ricci flow","authors":"Wangjian Jian, Jian Song","doi":"10.1007/s00039-022-00620-9","DOIUrl":"https://doi.org/10.1007/s00039-022-00620-9","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"32 1","pages":"1335 - 1356"},"PeriodicalIF":2.2,"publicationDate":"2022-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43085785","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}
Pub Date : 2022-08-04DOI: 10.1007/s00039-023-00634-x
Tristan C. Collins, Yang Li
{"title":"Uniqueness of some cylindrical tangent cones to special Lagrangians","authors":"Tristan C. Collins, Yang Li","doi":"10.1007/s00039-023-00634-x","DOIUrl":"https://doi.org/10.1007/s00039-023-00634-x","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"33 1","pages":"376-420"},"PeriodicalIF":2.2,"publicationDate":"2022-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49460197","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}
Pub Date : 2022-05-18DOI: 10.1007/s00039-022-00603-w
Pavel Etingof, Edward Frenkel, David Kazhdan
We continue to develop the analytic Langlands program for curves over local fields initiated in our earlier papers, following a suggestion of Langlands and a work of Teschner. Namely, we study the Hecke operators which we introduced in those papers in the case of a projective line with parabolic structures at finitely many points for the group (PGL_2). We establish most of our conjectures in this case.
{"title":"Analytic Langlands correspondence for $$PGL_2$$ P G L 2 on $${mathbb {P}}^1$$ P 1 with parabolic structures over local fields","authors":"Pavel Etingof, Edward Frenkel, David Kazhdan","doi":"10.1007/s00039-022-00603-w","DOIUrl":"https://doi.org/10.1007/s00039-022-00603-w","url":null,"abstract":"<p>We continue to develop the analytic Langlands program for curves over local fields initiated in our earlier papers, following a suggestion of Langlands and a work of Teschner. Namely, we study the Hecke operators which we introduced in those papers in the case of a projective line with parabolic structures at finitely many points for the group <span>(PGL_2)</span>. We establish most of our conjectures in this case.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"21 3 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516634","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}
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