发布求助
文献互助 智能选刊 最新文献

Geometric and Functional Analysis最新文献

筛选
英文 中文
The Asymptotic in Waring’s Problem over Function Fields via a Singular Locus in the Circle Method 基于圆上奇异轨迹的Waring问题的渐近性
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2026-04-04 DOI: 10.1007/s00039-026-00738-0
Will Sawin
{"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}
引用次数: 0
Asymptotic Behaviour of the Hitchin Metric on the Moduli Space of Higgs Bundles 希格斯束模空间上Hitchin度规的渐近性
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2026-04-04 DOI: 10.1007/s00039-026-00737-1
Takuro Mochizuki
{"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}
引用次数: 0
A Sharp Square Function Estimate for the Moment Curve in $mathbb{R}^{n}$ $mathbb{R}^{n}$中矩曲线的锐平方函数估计
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2026-03-11 DOI: 10.1007/s00039-026-00736-2
Larry Guth, Dominique Maldague
{"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}
引用次数: 0
Non ℝ-Covered Anosov Flows in Hyperbolic 3-Manifolds Are Quasigeodesic 双曲3-流形中非覆盖的Anosov流是拟拟椭球的
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2026-03-03 DOI: 10.1007/s00039-026-00733-5
Sergio R. Fenley
{"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}
引用次数: 0
Direct and Inverse Spectral Continuity for Dirac Operators 狄拉克算子的正、逆谱连续性
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2026-03-03 DOI: 10.1007/s00039-026-00735-3
R. V. Bessonov, P. V. Gubkin
{"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}
引用次数: 0
Contact Big Fiber Theorems 联系大纤维定理
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2026-02-25 DOI: 10.1007/s00039-026-00734-4
Yuhan Sun, Igor Uljarević, Umut Varolgunes
{"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}
引用次数: 0
Lossless Strichartz and Spectral Projection Estimates on Unbounded Manifolds 无界流形的无损Strichartz和谱投影估计
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2026-02-18 DOI: 10.1007/s00039-026-00732-6
Xiaoqi Huang, Christopher D. Sogge, Zhongkai Tao, Zhexing Zhang
{"title":"Lossless Strichartz and Spectral Projection Estimates on Unbounded Manifolds","authors":"Xiaoqi Huang, Christopher D. Sogge, Zhongkai Tao, Zhexing Zhang","doi":"10.1007/s00039-026-00732-6","DOIUrl":"https://doi.org/10.1007/s00039-026-00732-6","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"43 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146230757","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}
引用次数: 0
Strong Asymptotic Freeness of Haar Unitaries in Quasi-Exponential Dimensional Representations 准指数维表示中Haar酉的强渐近自由性
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2026-02-18 DOI: 10.1007/s00039-026-00730-8
Michael Magee, Mikael de la Salle
{"title":"Strong Asymptotic Freeness of Haar Unitaries in Quasi-Exponential Dimensional Representations","authors":"Michael Magee, Mikael de la Salle","doi":"10.1007/s00039-026-00730-8","DOIUrl":"https://doi.org/10.1007/s00039-026-00730-8","url":null,"abstract":"We prove almost sure strong asymptotic freeness of i.i.d. random unitaries with the following law: sample a Haar unitary matrix of dimension <jats:inline-formula> <jats:alternatives> <jats:tex-math>$n$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>n</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> and then send this unitary into an irreducible representation of <jats:inline-formula> <jats:alternatives> <jats:tex-math>$mathrm{U}(n)$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>U</mml:mi> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:math> </jats:alternatives> </jats:inline-formula> . The strong convergence holds as long as the irreducible representation arises from a pair of partitions of total size at most <jats:inline-formula> <jats:alternatives> <jats:tex-math>$n^{frac{1}{42}-varepsilon }$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>n</mml:mi> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mn>42</mml:mn> </mml:mfrac> <mml:mo>−</mml:mo> <mml:mi>ε</mml:mi> </mml:mrow> </mml:msup> </mml:math> </jats:alternatives> </jats:inline-formula> and is uniform in this regime. Previously this was known for partitions of total size up to <jats:inline-formula> <jats:alternatives> <jats:tex-math>$asymp log n/log log n$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>≍</mml:mo> <mml:mo>log</mml:mo> <mml:mi>n</mml:mi> <mml:mo>/</mml:mo> <mml:mo>log</mml:mo> <mml:mo>log</mml:mo> <mml:mi>n</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> by a result of Bordenave and Collins.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"50 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146230771","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}
引用次数: 0
Deformations of $mathbb{Z}_{2}$-Harmonic Spinors on 3-Manifolds 3-流形上$mathbb{Z}_{2}$-谐旋量的变形
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2026-02-16 DOI: 10.1007/s00039-026-00729-1
Gregory J. Parker
{"title":"Deformations of $mathbb{Z}_{2}$-Harmonic Spinors on 3-Manifolds","authors":"Gregory J. Parker","doi":"10.1007/s00039-026-00729-1","DOIUrl":"https://doi.org/10.1007/s00039-026-00729-1","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"20 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146204951","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}
引用次数: 0
Complete Classification of the Dehn Functions of Bestvina–Brady Groups Bestvina-Brady群Dehn函数的完全分类
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2026-02-02 DOI: 10.1007/s00039-026-00731-7
Yu-Chan Chang, Jerónimo García-Mejía, Matteo Migliorini
{"title":"Complete Classification of the Dehn Functions of Bestvina–Brady Groups","authors":"Yu-Chan Chang, Jerónimo García-Mejía, Matteo Migliorini","doi":"10.1007/s00039-026-00731-7","DOIUrl":"https://doi.org/10.1007/s00039-026-00731-7","url":null,"abstract":"We prove that the Dehn function of every finitely presented Bestvina–Brady group grows as a linear, quadratic, cubic, or quartic polynomial. In fact, we provide explicit criteria on the defining graph to determine the degree of this polynomial. As a consequence, we identify an obstruction that prevents certain Bestvina–Brady groups from admitting a CAT(0) structure.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"73 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146101776","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}
引用次数: 0
下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信
小红书