Proceedings of the American Mathematical Society最新文献

{"title":"On explicit abstract neutral differential equations with state-dependent delay II","authors":"Eduardo Hernández","doi":"10.1090/proc/16861","DOIUrl":"https://doi.org/10.1090/proc/16861","url":null,"abstract":"<p>We study the existence and uniqueness of strict solution for a general class of abstract explicit neutral equations with state-dependent delay. Some examples concerning explicit partial neutral differential equations with state dependent delay are presented.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"64 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Expansive partially hyperbolic diffeomorphisms with one-dimensional center","authors":"Martin Sambarino, José Vieitez","doi":"10.1090/proc/16845","DOIUrl":"https://doi.org/10.1090/proc/16845","url":null,"abstract":"<p>We give sufficient conditions for an expansive partially hyperbolic diffeomorphism with one-dimensional center to be (topologically) Anosov.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"135 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-realizability of some big mapping class groups","authors":"Lei Chen, Yan Mary He","doi":"10.1090/proc/16860","DOIUrl":"https://doi.org/10.1090/proc/16860","url":null,"abstract":"<p>In this note, we prove that the compactly supported mapping class group of a surface containing a genus <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=\"application/x-tex\">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> subsurface has no realization as a subgroup of the homeomorphism group. We also prove that for certain surfaces with order <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"6\"> <mml:semantics> <mml:mn>6</mml:mn> <mml:annotation encoding=\"application/x-tex\">6</mml:annotation> </mml:semantics> </mml:math> </inline-formula> symmetries, their mapping class groups have no realization as a subgroup of the homeomorphism group. Examples of such surfaces include the plane minus a Cantor set and the sphere minus a Cantor set.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"11 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Roots of unity and higher ramification in iterated extensions","authors":"Spencer Hamblen, Rafe Jones","doi":"10.1090/proc/16825","DOIUrl":"https://doi.org/10.1090/proc/16825","url":null,"abstract":"&lt;p&gt;Given a field &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;K&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;K&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, a rational function &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"phi element-of upper K left-parenthesis x right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;ϕ&lt;/mml:mi&gt; &lt;mml:mo&gt;∈&lt;/mml:mo&gt; &lt;mml:mi&gt;K&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;x&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;phi in K(x)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, and a point &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"b element-of double-struck upper P Superscript 1 Baseline left-parenthesis upper K right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;b&lt;/mml:mi&gt; &lt;mml:mo&gt;∈&lt;/mml:mo&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;P&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:msup&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;K&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;b in mathbb {P}^1(K)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, we study the extension &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K left-parenthesis phi Superscript negative normal infinity Baseline left-parenthesis b right-parenthesis right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;K&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;ϕ&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;−&lt;/mml:mo&gt; &lt;mml:mi mathvariant=\"normal\"&gt;∞&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:msup&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;b&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;K(phi ^{-infty }(b))&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; generated by the union over &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;n&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; of all solutions to &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"phi Superscript n Baseline left-parenthesis x right-parenthesis equals b\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;ϕ&lt;/mml:mi&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;x&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mi&gt;b&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;phi ^n(x) = b&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-for","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"68 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ergodic theorem for nonstationary random walks on compact abelian groups","authors":"Grigorii Monakov","doi":"10.1090/proc/16848","DOIUrl":"https://doi.org/10.1090/proc/16848","url":null,"abstract":"<p>We consider a nonstationary random walk on a compact metrizable abelian group. Under a classical strict aperiodicity assumption we establish a weak-* convergence to the Haar measure, Ergodic Theorem and Large Deviation Type Estimate.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"470 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global dynamics of epidemic network models via construction of Lyapunov functions","authors":"Rachidi Salako, Yixiang Wu","doi":"10.1090/proc/16872","DOIUrl":"https://doi.org/10.1090/proc/16872","url":null,"abstract":"<p>In this paper, we study the global dynamics of epidemic network models with standard incidence or mass-action transmission mechanism, when the dispersal of either the susceptible or the infected people is controlled. The connectivity matrix of the model is not assumed to be symmetric. Our main technique to study the global dynamics is to construct novel Lyapunov type functions.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"21 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Szegő recurrence for multiple orthogonal polynomials on the unit circle","authors":"Rostyslav Kozhan, Marcus Vaktnäs","doi":"10.1090/proc/16811","DOIUrl":"https://doi.org/10.1090/proc/16811","url":null,"abstract":"<p>We investigate polynomials that satisfy simultaneous orthogonality conditions with respect to several measures on the unit circle. We generalize the direct and inverse Szegő recurrence relations, identify the analogues of the Verblunsky coefficients, and prove the Christoffel–Darboux formula. These results should be viewed as the direct analogue of the nearest neighbour recurrence relations from the theory of multiple orthogonal polynomials on the real line.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"46 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Representations of groups on Banach spaces","authors":"Stefano Ferri, Camilo Gómez, Matthias Neufang","doi":"10.1090/proc/16499","DOIUrl":"https://doi.org/10.1090/proc/16499","url":null,"abstract":"&lt;p&gt;We establish a general framework for representability of a metric group on a (well-behaved) class of Banach spaces. More precisely, let &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper G\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"script\"&gt;G&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathcal {G}&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; be a topological group, and &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper A\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"script\"&gt;A&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathcal {A}&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; a unital symmetric &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript asterisk\"&gt; &lt;mml:semantics&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;C&lt;/mml:mi&gt; &lt;mml:mo&gt;∗&lt;!-- ∗ --&gt;&lt;/mml:mo&gt; &lt;/mml:msup&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;C^*&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-subalgebra of &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper U normal upper C left-parenthesis script upper G right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"normal\"&gt;U&lt;/mml:mi&gt; &lt;mml:mi mathvariant=\"normal\"&gt;C&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"script\"&gt;G&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathrm {UC}(mathcal {G})&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, the algebra of bounded uniformly continuous functions on &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper G\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"script\"&gt;G&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathcal {G}&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;. Generalizing the notion of a stable metric, we study &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper A\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"script\"&gt;A&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathcal {A}&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-metrics &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"delta\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;δ&lt;!-- δ --&gt;&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;delta&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, i.e., the function &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"delta left-parenthes","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"31 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Φ-moment inequalities for noncommutative differentially subordinate martingales","authors":"Yong Jiao, Mohammad Moslehian, Lian Wu, Yahui Zuo","doi":"10.1090/proc/16847","DOIUrl":"https://doi.org/10.1090/proc/16847","url":null,"abstract":"&lt;p&gt;We establish some &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Phi\"&gt; &lt;mml:semantics&gt; &lt;mml:mi mathvariant=\"normal\"&gt;Φ&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;Phi&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-moment inequalities for noncommutative differentially subordinate martingales. Let &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Phi\"&gt; &lt;mml:semantics&gt; &lt;mml:mi mathvariant=\"normal\"&gt;Φ&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;Phi&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; be a &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;p&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-convex and &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;q&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;q&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-concave Orlicz function with &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"1 greater-than p less-than-or-equal-to q greater-than 2\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;mml:mo&gt;&gt;&lt;/mml:mo&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;mml:mo&gt;≤&lt;/mml:mo&gt; &lt;mml:mi&gt;q&lt;/mml:mi&gt; &lt;mml:mo&gt;&gt;&lt;/mml:mo&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;1&gt;pleq q&gt;2&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;. Suppose that &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;x&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;x&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; and &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"y\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;y&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;y&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; are two self-adjoint martingales such that &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"y\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;y&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;y&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; is weakly differentially subordinate to &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;x&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;x&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;. We show that, for &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" al","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"27 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141516638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Obata-type formula and the Liouville-type theorem for a class of K-Hessian equations on the sphere","authors":"Shujun Shi, Peihe Wang, Tian Wu, Hua Zhu","doi":"10.1090/proc/16857","DOIUrl":"https://doi.org/10.1090/proc/16857","url":null,"abstract":"<p>In this paper, we study a class of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\"> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=\"application/x-tex\">k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Hessian equations, we can deduce an Obata-type formula and a Liouville-type theorem by integration by parts.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"19 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}