Transactions of the American Mathematical Society最新文献

{"title":"Soap bubbles and convex cones: optimal quantitative rigidity","authors":"Giorgio Poggesi","doi":"10.1090/tran/9207","DOIUrl":"https://doi.org/10.1090/tran/9207","url":null,"abstract":"<p>We consider a class of recent rigidity results in a convex cone <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Sigma subset-of-or-equal-to double-struck upper R Superscript upper N\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"normal\">Σ</mml:mi> <mml:mo>⊆</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mi>N</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Sigma subseteq mathbb {R}^N</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. These include overdetermined Serrin-type problems for a mixed boundary value problem relative to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Sigma\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Σ</mml:mi> <mml:annotation encoding=\"application/x-tex\">Sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, Alexandrov’s soap bubble-type results relative to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Sigma\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Σ</mml:mi> <mml:annotation encoding=\"application/x-tex\">Sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and Heintze-Karcher’s inequality relative to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Sigma\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Σ</mml:mi> <mml:annotation encoding=\"application/x-tex\">Sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Each rigidity result is obtained here by means of a single integral identity and holds true under weak integral overdeterminations in possibly non-smooth cones. Optimal quantitative stability estimates are obtained in terms of an <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L squared\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-pseudodistance. In particular, the optimal stability estimate for Heintze-Karcher’s inequality is new even in the classical case <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Sigma equals double-struck upper R Superscript upper N\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"normal\">Σ</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mi>N</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Sigma = mathbb {R}^N</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p> <p>Stability bounds in terms of the Hausdorff distance are also provided.</p> <p>Severa","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529542","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}

{"title":"Commensurated hyperbolic subgroups","authors":"Nir Lazarovich, Alex Margolis, Mahan Mj","doi":"10.1090/tran/9209","DOIUrl":"https://doi.org/10.1090/tran/9209","url":null,"abstract":"<p>We show that if <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H\"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding=\"application/x-tex\">H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a non-elementary hyperbolic commensurated subgroup of infinite index in a hyperbolic group <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, then <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H\"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding=\"application/x-tex\">H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is virtually a free product of hyperbolic surface groups and free groups. We prove that whenever a one-ended hyperbolic group <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H\"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding=\"application/x-tex\">H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a fiber of a non-trivial hyperbolic bundle then <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H\"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding=\"application/x-tex\">H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> virtually splits over a 2-ended subgroup.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743481","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}

{"title":"Endomorphisms of mapping tori","authors":"Christoforos Neofytidis","doi":"10.1090/tran/9203","DOIUrl":"https://doi.org/10.1090/tran/9203","url":null,"abstract":"<p>We classify in terms of Hopf-type properties mapping tori of residually finite Poincaré Duality groups with non-zero Euler characteristic. This generalises and gives a new proof of the analogous classification for fibered 3-manifolds. Various applications are given. In particular, we deduce that rigidity results for Gromov hyperbolic groups hold for the above mapping tori with trivial center.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529543","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}

{"title":"Solving the Kerzman’s problem on the sup-norm estimate for overline{∂} on product domains","authors":"Song-Ying Li","doi":"10.1090/tran/9208","DOIUrl":"https://doi.org/10.1090/tran/9208","url":null,"abstract":"<p>In this paper, the author solves the long term open problem of Kerzman on sup-norm estimate for Cauchy-Riemann equation on polydisc in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=\"application/x-tex\">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional complex space. The problem has been open since 1971. He also extends and solves the problem on product domains <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Omega Superscript n\"> <mml:semantics> <mml:msup> <mml:mi mathvariant=\"normal\">Ω</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">Omega ^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Omega\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Ω</mml:mi> <mml:annotation encoding=\"application/x-tex\">Omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is any bounded domain in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper C\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"double-struck\">C</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathbb {C}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript 1 comma alpha\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>α</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">C^{1,alpha }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> boundary for some <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"alpha greater-than 0\"> <mml:semantics> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">alpha &gt;0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506434","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}

{"title":"A compact extension of Journé’s 𝑇1 theorem on product spaces","authors":"Mingming Cao, Kôzô Yabuta, Dachun Yang","doi":"10.1090/tran/9206","DOIUrl":"https://doi.org/10.1090/tran/9206","url":null,"abstract":"<p>We prove a compact version of the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T Baseline 1\"> <mml:semantics> <mml:mrow> <mml:mi>T</mml:mi> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">T1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> theorem for bi-parameter singular integrals. That is, if a bi-parameter singular integral operator <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T\"> <mml:semantics> <mml:mi>T</mml:mi> <mml:annotation encoding=\"application/x-tex\">T</mml:annotation> </mml:semantics> </mml:math> </inline-formula> admits the compact full and partial kernel representations, and satisfies the weak compactness property, the diagonal <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C upper M upper O\"> <mml:semantics> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>M</mml:mi> <mml:mi>O</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">CMO</mml:annotation> </mml:semantics> </mml:math> </inline-formula> condition, and the product <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C upper M upper O\"> <mml:semantics> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>M</mml:mi> <mml:mi>O</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">CMO</mml:annotation> </mml:semantics> </mml:math> </inline-formula> condition, then <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T\"> <mml:semantics> <mml:mi>T</mml:mi> <mml:annotation encoding=\"application/x-tex\">T</mml:annotation> </mml:semantics> </mml:math> </inline-formula> can be extended to a compact operator on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript p Baseline left-parenthesis w right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>w</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">L^p(w)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for all <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"1 greater-than p greater-than normal infinity\"> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>&gt;</mml:mo> <mml:mi>p</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mi mathvariant=\"normal\">∞</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">1&gt;p&gt;infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"w element-of upper A Subscript p Baseline left-parenthesis double-s","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506433","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}

{"title":"Optimal convex domains for the first curl eigenvalue in dimension three","authors":"A. Enciso, Wadim Gerner, D. Peralta-Salas","doi":"10.1090/tran/8914","DOIUrl":"https://doi.org/10.1090/tran/8914","url":null,"abstract":"<p>We prove that there exists a bounded convex domain <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Omega subset-of double-struck upper R cubed\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi mathvariant=\"normal\">Ω</mml:mi>\u0000 <mml:mo>⊂</mml:mo>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">R</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>3</mml:mn>\u0000 </mml:msup>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Omega subset mathbb {R}^3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of fixed volume that minimizes the first positive curl eigenvalue among all other bounded convex domains of the same volume. We show that this optimal domain cannot be analytic, and that it cannot be stably convex if it is sufficiently smooth (e.g., of class <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript 1 comma 1\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>C</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">C^{1,1}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>). Existence results for uniformly Hölder optimal domains in a box (that is, contained in a fixed bounded domain <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper D subset-of double-struck upper R cubed\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>D</mml:mi>\u0000 <mml:mo>⊂</mml:mo>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">R</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>3</mml:mn>\u0000 </mml:msup>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Dsubset mathbb {R}^3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>) are also presented.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140664498","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}

{"title":"Separating path systems of almost linear size","authors":"Shoham Letzter","doi":"10.1090/tran/9187","DOIUrl":"https://doi.org/10.1090/tran/9187","url":null,"abstract":"<p>A <italic>separating path system</italic> for a graph <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a collection <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper P\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"script\">P</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal {P}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of paths in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that for every two edges <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"e\"> <mml:semantics> <mml:mi>e</mml:mi> <mml:annotation encoding=\"application/x-tex\">e</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\"> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=\"application/x-tex\">f</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, there is a path in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper P\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"script\">P</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal {P}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> that contains <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"e\"> <mml:semantics> <mml:mi>e</mml:mi> <mml:annotation encoding=\"application/x-tex\">e</mml:annotation> </mml:semantics> </mml:math> </inline-formula> but not <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\"> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=\"application/x-tex\">f</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that every <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=\"application/x-tex\">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-vertex graph has a separating path system of size <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper O left-parenthesis n log Superscript asterisk Baseline n right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532721","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}

{"title":"On a conjectural symmetric version of Ehrhard’s inequality","authors":"Galyna Livshyts","doi":"10.1090/tran/9177","DOIUrl":"https://doi.org/10.1090/tran/9177","url":null,"abstract":"<p>We formulate a plausible conjecture for the optimal Ehrhard-type inequality for convex symmetric sets with respect to the Gaussian measure. Namely, letting <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper J Subscript k minus 1 Baseline left-parenthesis s right-parenthesis equals integral Subscript 0 Superscript s Baseline t Superscript k minus 1 Baseline e Superscript minus StartFraction t squared Over 2 EndFraction Baseline d t\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>s</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mo>∫</mml:mo> <mml:mn>0</mml:mn> <mml:mi>s</mml:mi> </mml:msubsup> <mml:msup> <mml:mi>t</mml:mi> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mfrac> <mml:msup> <mml:mi>t</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:msup> <mml:mi>d</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">J_{k-1}(s)=int ^s_0 t^{k-1} e^{-frac {t^2}{2}}dt</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"c Subscript k minus 1 Baseline equals upper J Subscript k minus 1 Baseline left-parenthesis plus normal infinity right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>c</mml:mi> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>J</mml:mi> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mo>+</mml:mo> <mml:mi mathvariant=\"normal\">∞</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">c_{k-1}=J_{k-1}(+infty )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we conjecture that the function <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F colon left-bracket 0 comma 1 right-bracket right-arrow double-struck upper R\"> <mml:semantics> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo>:</mml:mo> <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:mo stretchy=\"false\">→</mml:mo> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">F:[0,1]rightarrow mathbb {R}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, given by <disp-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F left-parent","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152962","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}

{"title":"Colength one deformation rings","authors":"Daniel Le, Bao Le Hung, Stefano Morra, Chol Park, Zicheng Qian","doi":"10.1090/tran/9191","DOIUrl":"https://doi.org/10.1090/tran/9191","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K slash double-struck upper Q Subscript p\"> <mml:semantics> <mml:mrow> <mml:mi>K</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant=\"double-struck\">Q</mml:mi> </mml:mrow> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">K/mathbb {Q}_p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a finite unramified extension, <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"rho overbar colon normal upper G normal a normal l left-parenthesis double-struck upper Q overbar Subscript p Baseline slash upper K right-parenthesis right-arrow normal upper G normal upper L Subscript n Baseline left-parenthesis double-struck upper F overbar Subscript p Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mover> <mml:mi>ρ</mml:mi> <mml:mo accent=\"false\">¯</mml:mo> </mml:mover> <mml:mo>:</mml:mo> <mml:mrow> <mml:mi mathvariant=\"normal\">G</mml:mi> <mml:mi mathvariant=\"normal\">a</mml:mi> <mml:mi mathvariant=\"normal\">l</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msub> <mml:mover> <mml:mrow> <mml:mi mathvariant=\"double-struck\">Q</mml:mi> </mml:mrow> <mml:mo accent=\"false\">¯</mml:mo> </mml:mover> <mml:mi>p</mml:mi> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>K</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">→</mml:mo> <mml:msub> <mml:mrow> <mml:mi mathvariant=\"normal\">G</mml:mi> <mml:mi mathvariant=\"normal\">L</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msub> <mml:mover> <mml:mrow> <mml:mi mathvariant=\"double-struck\">F</mml:mi> </mml:mrow> <mml:mo accent=\"false\">¯</mml:mo> </mml:mover> <mml:mi>p</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">overline {rho }:mathrm {Gal}(overline {mathbb {Q}}_p/K)rightarrow mathrm {GL}_n(overline {mathbb {F}}_p)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a continuous representation, and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"tau\"> <mml:semantics> <mml:mi>τ</mml:mi> <mml:annotation encoding=\"application/x-tex\">tau</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a tame inertial type of dimension <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=\"application/x-tex\">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We explicitly determine, under mild regularity conditions on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"tau\"> <mml:semantics> <mml:mi>τ</mml:mi> <mml:annotation encoding=\"","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060514","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}

{"title":"Polynomial decay of correlations for nonpositively curved surfaces","authors":"Yuri Lima, Carlos Matheus, Ian Melbourne","doi":"10.1090/tran/9182","DOIUrl":"https://doi.org/10.1090/tran/9182","url":null,"abstract":"<p>We prove polynomial decay of correlations for geodesic flows on a class of nonpositively curved surfaces where zero curvature only occurs along one closed geodesic. We also prove that various statistical limit laws, including the central limit theorem, are satisfied by this class of geodesic flows.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519505","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}