Geometric and Functional Analysis最新文献

{"title":"A New Notion of Dimension for Dynamical Systems and Shift Embeddability","authors":"Tom Meyerovitch","doi":"10.1007/s00039-026-00742-4","DOIUrl":"https://doi.org/10.1007/s00039-026-00742-4","url":null,"abstract":"A dynamical system <inline-formula><alternatives><mml:math><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$(X,T)$end{document}</tex-math></alternatives></inline-formula> is <italic>shift embeddable</italic> if <inline-formula><alternatives><mml:math><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$(X,T)$end{document}</tex-math></alternatives></inline-formula> embeds continuously and equivariantly in the shift over <inline-formula><alternatives><mml:math><mml:msup><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow><mml:mi>d</mml:mi></mml:msup></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$[0,1]^{d}$end{document}</tex-math></alternatives></inline-formula> for some finite <inline-formula><alternatives><mml:math><mml:mi>d</mml:mi></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$d$end{document}</tex-math></alternatives></inline-formula>. Refuting a major conjecture in the field, in a recent result of Dranishnikov and Levin it was shown that Gromov’s mean dimension and Lebesgue covering dimension of finite orbits are not the only obstructions for shift embeddability. We present a new notion of dimension for dynamical systems over any countable group. We show that this new notion of dimension accounts for all known obstructions for shift embeddability.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"19 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148612833","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}

{"title":"Endoscopic Decomposition of Elliptic Fargues–Scholze Ldocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$L$end{document}-Packets","authors":"David Kazhdan, Yakov Varshavsky","doi":"10.1007/s00039-026-00741-5","DOIUrl":"https://doi.org/10.1007/s00039-026-00741-5","url":null,"abstract":"The main goal of this note is to show that the local <inline-formula><alternatives><mml:math><mml:mi>L</mml:mi></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$L$end{document}</tex-math></alternatives></inline-formula>-packets of Fargues–Scholze [<xref ref-type=\"bibr\">FS21</xref>], corresponding to elliptic <inline-formula><alternatives><mml:math><mml:mi>L</mml:mi></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$L$end{document}</tex-math></alternatives></inline-formula>-parameters, admit an endoscopic decomposition. Our argument is strongly motivated by a beautiful paper of Chenji Fu [<xref ref-type=\"bibr\">Fu25</xref>], where the stable case is proven.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"19 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148612834","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}

{"title":"Effective Mapping Class Group Dynamics II: Geometric Intersection Numbers","authors":"Francisco Arana–Herrera","doi":"10.1007/s00039-026-00740-6","DOIUrl":"https://doi.org/10.1007/s00039-026-00740-6","url":null,"abstract":"We show that the action of the mapping class group on the space of closed curves of a closed surface effectively tracks the corresponding action on Teichmüller space in the following sense: for all but quantitatively few mapping classes, the information of how a mapping class moves a given point of Teichmüller space determines, up to a power saving error term, how it changes the geometric intersection numbers of a given closed curve with respect to arbitrary geodesic currents. Applications include an effective estimate describing the speed of convergence of Teichmüller geodesic rays to the boundary at infinity of Teichmüller space, an effective estimate comparing the Teichmüller and Thurston metrics along mapping class group orbits of Teichmüller space, and, in the sequel and forthcoming work of Honaryar, effective estimates for countings of closed geodesics on closed, negatively curved surfaces. Furthermore, in forthcoming work of Arana-Herrera and Honaryar, the main result of this paper is applied to study the arithmetic/homological complexity of long simple closed geodesics on negatively curved surfaces.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"17 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148612835","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}

{"title":"Length of a Closed Geodesic in 3-Manifolds of Positive Scalar Curvature","authors":"Yevgeny Liokumovich, Davi Maximo, Regina Rotman","doi":"10.1007/s00039-026-00739-z","DOIUrl":"https://doi.org/10.1007/s00039-026-00739-z","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"22 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285851","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}

{"title":"The Asymptotic in Waring’s Problem over Function Fields via a Singular Locus in the Circle Method","authors":"Will Sawin","doi":"10.1007/s00039-026-00738-0","DOIUrl":"https://doi.org/10.1007/s00039-026-00738-0","url":null,"abstract":"We give results on the asymptotic in Waring’s problem over function fields that are stronger than the results obtained over the integers using the main conjecture in Vinogradov’s mean value theorem. Similar estimates apply to Manin’s conjecture for Fermat hypersurfaces over function fields. Following an idea of Pugin, rather than applying analytic methods to estimate the minor arcs, we treat them as complete exponential sums over finite fields and apply results of Katz, which bound the sum in terms of the dimension of a certain singular locus, which we estimate by tangent space calculations.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"65 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147702354","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}

{"title":"Asymptotic Behaviour of the Hitchin Metric on the Moduli Space of Higgs Bundles","authors":"Takuro Mochizuki","doi":"10.1007/s00039-026-00737-1","DOIUrl":"https://doi.org/10.1007/s00039-026-00737-1","url":null,"abstract":"The moduli space of stable Higgs bundles of degree 0 is equipped with the hyperkähler metric, called the Hitchin metric. On the locus where the spectral curves are smooth, there is the hyperkähler metric called the semi-flat metric, associated with the algebraic integrable systems with the Hitchin section. We prove the exponentially rapid decay of the difference between the Hitchin metric and the semi-flat metric along the ray <inline-formula><alternatives><mml:math><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>E</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mi>θ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$(E,ttheta )$end{document}</tex-math></alternatives></inline-formula> as <inline-formula><alternatives><mml:math><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mi mathvariant=\"normal\">∞</mml:mi></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$tto infty $end{document}</tex-math></alternatives></inline-formula>.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"125 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147702355","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}

{"title":"A Sharp Square Function Estimate for the Moment Curve in $mathbb{R}^{n}$","authors":"Larry Guth, Dominique Maldague","doi":"10.1007/s00039-026-00736-2","DOIUrl":"https://doi.org/10.1007/s00039-026-00736-2","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"10 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147461911","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}

{"title":"Non ℝ-Covered Anosov Flows in Hyperbolic 3-Manifolds Are Quasigeodesic","authors":"Sergio R. Fenley","doi":"10.1007/s00039-026-00733-5","DOIUrl":"https://doi.org/10.1007/s00039-026-00733-5","url":null,"abstract":"The main result is that if an Anosov flow in a closed hyperbolic three manifold is not <inline-formula><alternatives><mml:math><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$mbox{${mathbb{R}}$}$end{document}</tex-math></alternatives></inline-formula>-covered, then the flow is a quasigeodesic flow. We also prove that if a hyperbolic three manifold supports an Anosov flow, then up to a double cover it supports a quasigeodesic flow. We prove the continuous extension property for the stable and unstable foliations of any Anosov flow in a closed hyperbolic three manifold, and the existence of group invariant Peano curves associated with any such flow.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"47 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147702357","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}

{"title":"Direct and Inverse Spectral Continuity for Dirac Operators","authors":"R. V. Bessonov, P. V. Gubkin","doi":"10.1007/s00039-026-00735-3","DOIUrl":"https://doi.org/10.1007/s00039-026-00735-3","url":null,"abstract":"The half-line Dirac operators with <inline-formula><alternatives><mml:math><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$L^{2}$end{document}</tex-math></alternatives></inline-formula>-potentials can be characterized by their spectral data. It is known that the spectral correspondence is a homeomorphism: close potentials give rise to close spectral data and vice versa. We prove the first explicit two-sided uniform estimate related to this continuity in the general <inline-formula><alternatives><mml:math><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$L^{2}$end{document}</tex-math></alternatives></inline-formula>-case. The proof is based on an exact solution of the inverse spectral problem for Dirac operators with <inline-formula><alternatives><mml:math><mml:mi>δ</mml:mi></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$delta $end{document}</tex-math></alternatives></inline-formula>-interactions on a half-lattice in terms of the Schur’s algorithm for analytic functions.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"6 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147702356","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}

{"title":"Contact Big Fiber Theorems","authors":"Yuhan Sun, Igor Uljarević, Umut Varolgunes","doi":"10.1007/s00039-026-00734-4","DOIUrl":"https://doi.org/10.1007/s00039-026-00734-4","url":null,"abstract":"We prove contact big fiber theorems, analogous to the symplectic big fiber theorem by Entov and Polterovich, using symplectic cohomology with support. Unlike in the symplectic case, the validity of the statements requires conditions on the closed contact manifold. One such condition is to admit a Liouville filling with non-zero symplectic cohomology. In the case of Boothby-Wang contact manifolds, we prove the result under the condition that the Euler class of the circle bundle, which is the negative of an integral lift of the symplectic class, is not an invertible element in the quantum cohomology of the base symplectic manifold. As applications, we obtain new examples of rigidity of intersections in contact manifolds and also of contact non-squeezing.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"128 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147287144","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}