Expositiones Mathematicae最新文献

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Expository article: “Bounded orthogonal systems and the Λ(p)-set problem” by Jean Bourgain 说明性文章:“有界正交系统和Λ(p)-集问题”,作者:Jean Bourgain
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2025-04-16 DOI: 10.1016/j.exmath.2025.125691
Hongki Jung , Bartosz Langowski , Alexander Ortiz , Truong Vu
{"title":"Expository article: “Bounded orthogonal systems and the Λ(p)-set problem” by Jean Bourgain","authors":"Hongki Jung ,&nbsp;Bartosz Langowski ,&nbsp;Alexander Ortiz ,&nbsp;Truong Vu","doi":"10.1016/j.exmath.2025.125691","DOIUrl":"10.1016/j.exmath.2025.125691","url":null,"abstract":"<div><div>In this paper, we present an exposition of the work by Jean Bourgain, in which he resolved the well known conjecture posed by Rudin regarding the existence of <span><math><mrow><mi>Λ</mi><mrow><mo>(</mo><mi>p</mi><mo>)</mo></mrow></mrow></math></span>-sets.</div></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"43 5","pages":"Article 125691"},"PeriodicalIF":0.8,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 comprehensive approach to multifractal analysis 多重分形分析的综合方法
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2025-04-11 DOI: 10.1016/j.exmath.2025.125690
Zhiming Li , Bilel Selmi , Haythem Zyoudi
{"title":"A comprehensive approach to multifractal analysis","authors":"Zhiming Li ,&nbsp;Bilel Selmi ,&nbsp;Haythem Zyoudi","doi":"10.1016/j.exmath.2025.125690","DOIUrl":"10.1016/j.exmath.2025.125690","url":null,"abstract":"<div><div>This paper investigates how specific techniques have been broadened to suit more general contexts. Among them, multifractal analysis stands out for its adaptability and depth, presenting a unified framework to approach these generalizations. We examine the relative multifractal formalism within the context of metric spaces in a general way. The primary aim is to introduce a generalized concept of general relative multifractal Hausdorff and packing measures. In particular, we delve into the characteristics of the generalized multifractal Hausdorff and packing measures and analyze their impact on the broader multifractal spectrum functions. The investigation explores the connection between these generalized multifractal measures and the nature of general multifractal dimensions within this framework. Further, we establish an equivalence relation between general relative multifractal Hausdorff and packing measures by utilizing density theorems. Moreover, we study various properties of the generalized relative multifractal Hausdorff measures, packing measures, and pre-measures. Lastly, our work addresses the question of whether a subset in Euclidean space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> with infinite positive Hausdorff measure can contain a compact set of positive finite general relative Hausdorff measures.</div></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"43 5","pages":"Article 125690"},"PeriodicalIF":0.8,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On a criterion for algebraic independence applied to continued fractions 应用于连分式的代数无关性判据
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2025-04-10 DOI: 10.1016/j.exmath.2025.125689
Gessica Alecci , Carsten Elsner
{"title":"On a criterion for algebraic independence applied to continued fractions","authors":"Gessica Alecci ,&nbsp;Carsten Elsner","doi":"10.1016/j.exmath.2025.125689","DOIUrl":"10.1016/j.exmath.2025.125689","url":null,"abstract":"<div><div>From around 2010 onward, Elsner et al.<!--> <!--> <!-->developed and applied a method in which the algebraic independence of <span><math><mi>n</mi></math></span> quantities <span><math><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span> over a field is transferred to further <span><math><mi>n</mi></math></span> quantities <span><math><mrow><msub><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span> by means of a system of polynomials in <span><math><mrow><mn>2</mn><mi>n</mi></mrow></math></span> variables <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><msub><mrow><mi>Y</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span>. In this paper, we systematically study and explain this criterion and its variants. Moreover, we present new results concerning its application to periodic non-regular continued fractions, namely continued fractions with real numbers as partial quotients. We show that given a continued fraction of this type, this criterion can be applied to prove that not only are the convergents algebraically independent from each other, but they are also algebraically independent from the continued fraction.</div></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"43 5","pages":"Article 125689"},"PeriodicalIF":0.8,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Jordan homomorphisms on Hilbert C∗-modules Hilbert C * -模上的Jordan同态
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2025-04-03 DOI: 10.1016/j.exmath.2025.125687
Xiaofei Qi , Huimin Chen , Jinchuan Hou
{"title":"Jordan homomorphisms on Hilbert C∗-modules","authors":"Xiaofei Qi ,&nbsp;Huimin Chen ,&nbsp;Jinchuan Hou","doi":"10.1016/j.exmath.2025.125687","DOIUrl":"10.1016/j.exmath.2025.125687","url":null,"abstract":"<div><div>We generalize the concept of homomorphisms between Hilbert C<span><math><msup><mrow></mrow><mrow><mo>∗</mo></mrow></msup></math></span>-modules to the concept of Jordan homomorphisms. Let <span><math><mi>M</mi></math></span> be a Hilbert C<span><math><msup><mrow></mrow><mrow><mo>∗</mo></mrow></msup></math></span>-module over a C<span><math><msup><mrow></mrow><mrow><mo>∗</mo></mrow></msup></math></span>-algebra <span><math><mi>A</mi></math></span> and <span><math><mrow><mi>φ</mi><mo>:</mo><mi>M</mi><mo>→</mo><mi>M</mi></mrow></math></span> be a map. Under the condition that <span><math><mi>A</mi></math></span> is commutative and <span><math><mi>φ</mi></math></span> is <span><math><mi>ℂ</mi></math></span>-linear bounded, we show that <span><math><mi>φ</mi></math></span> is a Jordan homomorphism if and only if <span><math><mi>φ</mi></math></span> is a homomorphism. In addition, we also discuss the relationship between <span><math><mi>Φ</mi></math></span>-unitary maps and automorphisms, and give some conditions under which <span><math><mi>φ</mi></math></span> is an automorphism if and only if <span><math><mi>φ</mi></math></span> is a <span><math><mi>Φ</mi></math></span>-unitary map.</div></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"43 4","pages":"Article 125687"},"PeriodicalIF":0.8,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The redundancy of Gabor type unitary systems on locally compact abelian groups 局部紧阿贝尔群上Gabor型酉系统的冗余性
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2025-04-03 DOI: 10.1016/j.exmath.2025.125686
Jingsheng Wang, Pengtong Li
{"title":"The redundancy of Gabor type unitary systems on locally compact abelian groups","authors":"Jingsheng Wang,&nbsp;Pengtong Li","doi":"10.1016/j.exmath.2025.125686","DOIUrl":"10.1016/j.exmath.2025.125686","url":null,"abstract":"<div><div>In this paper, we extend the redundancy theorem of J. Gabardo and D. Han for Gabor type unitary systems indexed by full-rank lattices in Euclidean spaces to the setting of locally compact abelian (LCA) groups. Let <span><math><mi>G</mi></math></span> be an LCA group, let <span><math><mi>Λ</mi></math></span> be a uniform lattice in <span><math><mi>G</mi></math></span>, let <span><math><mi>α</mi></math></span> be an automorphism of <span><math><mi>G</mi></math></span>, and let <span><math><mi>β</mi></math></span> be an automorphism of <span><math><mover><mrow><mi>G</mi></mrow><mrow><mo>̂</mo></mrow></mover></math></span>. We show that the redundancy of a Gabor type unitary system indexed by <span><math><mrow><mi>α</mi><mrow><mo>(</mo><mi>Λ</mi><mo>)</mo></mrow><mo>×</mo><mi>β</mi><mrow><mo>(</mo><msup><mrow><mi>Λ</mi></mrow><mrow><mo>⊥</mo></mrow></msup><mo>)</mo></mrow></mrow></math></span> equals the reciprocal of the density of this index set. As an application, we give a new proof of the famous time-frequency density theorem in Gabor analysis.</div></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"43 4","pages":"Article 125686"},"PeriodicalIF":0.8,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Generalized Fermat equation: A survey of solved cases 广义费马方程:已解案例综述
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2025-04-03 DOI: 10.1016/j.exmath.2025.125688
Ashleigh Ratcliffe, Bogdan Grechuk
{"title":"Generalized Fermat equation: A survey of solved cases","authors":"Ashleigh Ratcliffe,&nbsp;Bogdan Grechuk","doi":"10.1016/j.exmath.2025.125688","DOIUrl":"10.1016/j.exmath.2025.125688","url":null,"abstract":"<div><div>Generalized Fermat equation (GFE) is the equation of the form <span><math><mrow><mi>a</mi><msup><mrow><mi>x</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>+</mo><mi>b</mi><msup><mrow><mi>y</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>=</mo><mi>c</mi><msup><mrow><mi>z</mi></mrow><mrow><mi>r</mi></mrow></msup></mrow></math></span>, where <span><math><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>,</mo><mi>r</mi></mrow></math></span> are positive integers. If <span><math><mrow><mn>1</mn><mo>/</mo><mi>p</mi><mo>+</mo><mn>1</mn><mo>/</mo><mi>q</mi><mo>+</mo><mn>1</mn><mo>/</mo><mi>r</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>, GFE is known to have at most finitely many primitive integer solutions <span><math><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo></mrow></math></span>. A large body of the literature is devoted to finding such solutions explicitly for various six-tuples <span><math><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>,</mo><mi>r</mi><mo>)</mo></mrow></math></span>, as well as for infinite families of such six-tuples. This paper surveys the families of parameters for which GFE has been solved. Although the proofs are not discussed here, collecting these references in one place will make it easier for the readers to find the relevant proof techniques in the original papers. Also, this survey will help the readers to avoid duplicate work by solving the already solved cases.</div></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"43 4","pages":"Article 125688"},"PeriodicalIF":0.8,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143839742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Symmetrized pseudofunction algebras from Lp-representations and amenability of locally compact groups lp -表示的对称伪函数代数与局部紧群的可调性
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2025-04-02 DOI: 10.1016/j.exmath.2025.125685
Emilie Mai Elkiær
{"title":"Symmetrized pseudofunction algebras from Lp-representations and amenability of locally compact groups","authors":"Emilie Mai Elkiær","doi":"10.1016/j.exmath.2025.125685","DOIUrl":"10.1016/j.exmath.2025.125685","url":null,"abstract":"<div><div>We show via an application of techniques from complex interpolation theory how the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-pseudofunction algebras of a locally compact group <span><math><mi>G</mi></math></span> can be understood as sitting between <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msup><mrow><mi>C</mi></mrow><mrow><mo>∗</mo></mrow></msup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. Motivated by this, we collect and review various characterizations of group amenability connected to the <span><math><mi>p</mi></math></span>-pseudofunction algebra of Herz and generalize these to the symmetrized setting. Along the way, we describe the Banach space dual of the symmetrized pseudofunction algebras on <span><math><mi>G</mi></math></span> associated with representations on reflexive Banach spaces.</div></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"43 4","pages":"Article 125685"},"PeriodicalIF":0.8,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143820722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Linearization of Lipschitz framings for Banach spaces Banach空间的Lipschitz框架的线性化
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2025-04-01 DOI: 10.1016/j.exmath.2025.125680
Qiyao Bao , Deguang Han , Rui Liu , Jie Shen
{"title":"Linearization of Lipschitz framings for Banach spaces","authors":"Qiyao Bao ,&nbsp;Deguang Han ,&nbsp;Rui Liu ,&nbsp;Jie Shen","doi":"10.1016/j.exmath.2025.125680","DOIUrl":"10.1016/j.exmath.2025.125680","url":null,"abstract":"<div><div>Nonlinear framings naturally appear in many applications where nonlinear procedures are necessary. This paper examines two basic issues involving the linearization of Lipschitz framings. We first prove that every Lipschitz framing induces a linear framing which shares the same synthesis operator, and consequently every Banach space admitting a Lipschitz framing has the bounded approximation property. Secondly, we examine the projection-valued dilations of Lipschitz operator-valued measures on Banach spaces. We prove that every Lipschitz operator-valued measure can induce an operator-valued measure by linearization, and every <span><math><mrow><mi>Lip</mi><mrow><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></mrow></mrow></math></span>-valued measure has a projection-valued measure dilation by establishing a nonlinear version of minimal dilation theory. As examples, we discuss a concrete construction of the minimal dilation for the special case when the measure space is <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo></mrow></math></span>, and how nonlinear sampling naturally induces a Lipschitz framing.</div></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"43 4","pages":"Article 125680"},"PeriodicalIF":0.8,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Divisibility of orders of reductions of elliptic curves 椭圆曲线约简阶的可整除性
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2025-03-27 DOI: 10.1016/j.exmath.2025.125679
Antigona Pajaziti , Mohammad Sadek
{"title":"Divisibility of orders of reductions of elliptic curves","authors":"Antigona Pajaziti ,&nbsp;Mohammad Sadek","doi":"10.1016/j.exmath.2025.125679","DOIUrl":"10.1016/j.exmath.2025.125679","url":null,"abstract":"<div><div>Let <span><math><mi>E</mi></math></span> be an elliptic curve defined over <span><math><mi>Q</mi></math></span> and <span><math><msub><mrow><mover><mrow><mi>E</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>p</mi></mrow></msub></math></span> denote the reduction of <span><math><mi>E</mi></math></span> modulo a prime <span><math><mi>p</mi></math></span> of good reduction for <span><math><mi>E</mi></math></span>. The divisibility of <span><math><mrow><mo>|</mo><msub><mrow><mover><mrow><mi>E</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>p</mi></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>)</mo></mrow><mo>|</mo></mrow></math></span> by an integer <span><math><mrow><mi>m</mi><mo>≥</mo><mn>2</mn></mrow></math></span> for a set of primes <span><math><mi>p</mi></math></span> of density 1 is determined by the torsion subgroups of elliptic curves that are <span><math><mi>Q</mi></math></span>-isogenous to <span><math><mi>E</mi></math></span>. In this work, we give explicit families of elliptic curves <span><math><mi>E</mi></math></span> over <span><math><mi>Q</mi></math></span> together with integers <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>E</mi></mrow></msub></math></span> such that the congruence class of <span><math><mrow><mo>|</mo><msub><mrow><mover><mrow><mi>E</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>p</mi></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>)</mo></mrow><mo>|</mo></mrow></math></span> modulo <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>E</mi></mrow></msub></math></span> can be computed explicitly. In addition, we can estimate the density of primes <span><math><mi>p</mi></math></span> for which each congruence class occurs. These include elliptic curves over <span><math><mi>Q</mi></math></span> whose torsion grows over a quadratic field <span><math><mi>K</mi></math></span> where <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>E</mi></mrow></msub></math></span> is determined by the <span><math><mi>K</mi></math></span>-torsion subgroups in the <span><math><mi>Q</mi></math></span>-isogeny class of <span><math><mi>E</mi></math></span>. We also exhibit elliptic curves over <span><math><mrow><mi>Q</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> for which the orders of the reductions of every smooth fiber modulo primes of positive density strictly less than 1 are divisible by given small integers.</div></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"43 4","pages":"Article 125679"},"PeriodicalIF":0.8,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms 胶合微分同态,双lipschitz映射与同胚
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2025-03-25 DOI: 10.1016/j.exmath.2025.125681
Paweł Goldstein , Zofia Grochulska , Piotr Hajłasz
{"title":"Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms","authors":"Paweł Goldstein ,&nbsp;Zofia Grochulska ,&nbsp;Piotr Hajłasz","doi":"10.1016/j.exmath.2025.125681","DOIUrl":"10.1016/j.exmath.2025.125681","url":null,"abstract":"<div><div>Cerf and Palais independently proved a remarkable result about extending diffeomorphisms defined on smooth balls in a manifold to global diffeomorphisms of the manifold onto itself. We explain Palais’ argument and show how to extend it to the class of homeomorphisms and bi-Lipschitz homeomorphisms. While Palais’ argument is surprising, it is elementary and short. However, its extension to bi-Lipschitz homeomorphisms and homeomorphisms requires deep results: the stable homeomorphism and the annulus theorems.</div></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"43 4","pages":"Article 125681"},"PeriodicalIF":0.8,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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