Proceedings of the American Mathematical Society最新文献

{"title":"A note on almalgamated free products","authors":"Qihui Li, Don Hadwin, Junhao Shen","doi":"10.1090/proc/16791","DOIUrl":"https://doi.org/10.1090/proc/16791","url":null,"abstract":"<p>We prove a general result concerning properties preserved under certain amalgamated free products.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151831","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":"Radon–Nikodým property and Lau’s conjecture","authors":"Andrzej Wiśnicki","doi":"10.1090/proc/16884","DOIUrl":"https://doi.org/10.1090/proc/16884","url":null,"abstract":"<p>There is a long-standing problem, posed by A.T.-M. Lau [<italic>Fixed point theory and its applications</italic>, Academic Press, New York-London, 1976, pp. 121–129], whether left amenability is sufficient to ensure the existence of a common fixed point for every jointly weak<inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"Superscript asterisk\"> <mml:semantics> <mml:msup> <mml:mi/> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">^{ast }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> continuous nonexpansive semigroup action on a nonempty weak<inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"Superscript asterisk\"> <mml:semantics> <mml:msup> <mml:mi/> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">^{ast }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> compact convex set in a dual Banach space. In this note we discuss the current status of this problem and give a partial solution in the case of weak<inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"Superscript asterisk\"> <mml:semantics> <mml:msup> <mml:mi/> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">^{ast }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> compact convex sets with the Radon–Nikodým property.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872178","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":"Hyperfiniteness for group actions on trees","authors":"Srivatsav Kunnawalkam Elayavalli, Koichi Oyakawa, Forte Shinko, Pieter Spaas","doi":"10.1090/proc/16851","DOIUrl":"https://doi.org/10.1090/proc/16851","url":null,"abstract":"<p>We identify natural conditions for a countable group acting on a countable tree which imply that the orbit equivalence relation of the induced action on the Gromov boundary is Borel hyperfinite. Examples of this condition include acylindrical actions. We also identify a natural weakening of the aforementioned conditions that implies measure hyperfiniteness of the boundary action. We then document examples of group actions on trees whose boundary action is not hyperfinite.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744759","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":"Strichartz type estimates for solutions to the Schrödinger equation","authors":"Jie Chen","doi":"10.1090/proc/16887","DOIUrl":"https://doi.org/10.1090/proc/16887","url":null,"abstract":"<p>In this article, we show the necessary and sufficient conditions for the inequality <disp-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-vertical-bar u double-vertical-bar Subscript upper L Sub Subscript t Sub Superscript q Subscript upper L Sub Subscript x Sub Superscript r Subscript Baseline less-than-or-equivalent-to double-vertical-bar u double-vertical-bar Subscript upper X Sub Superscript s comma b Subscript Baseline comma\"> <mml:semantics> <mml:mrow> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mi>u</mml:mi> <mml:msub> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mrow> <mml:msubsup> <mml:mi>L</mml:mi> <mml:mi>t</mml:mi> <mml:mi>q</mml:mi> </mml:msubsup> <mml:msubsup> <mml:mi>L</mml:mi> <mml:mi>x</mml:mi> <mml:mi>r</mml:mi> </mml:msubsup> </mml:mrow> </mml:msub> <mml:mo>≲</mml:mo> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mi>u</mml:mi> <mml:msub> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mrow> <mml:msup> <mml:mi>X</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">begin{equation*} |u|_{L_t^qL_x^r}lesssim |u|_{X^{s,b}}, end{equation*}</mml:annotation> </mml:semantics> </mml:math> </disp-formula> where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-vertical-bar u double-vertical-bar Subscript upper X Sub Superscript s comma b Baseline colon-equal double-vertical-bar ModifyingAbove u With caret left-parenthesis tau comma xi right-parenthesis mathematical left-angle xi mathematical right-angle Superscript s Baseline mathematical left-angle tau plus StartAbsoluteValue xi EndAbsoluteValue squared mathematical right-angle Superscript b Baseline double-vertical-bar Subscript upper L Sub Subscript tau comma xi Sub Superscript 2\"> <mml:semantics> <mml:mrow> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mi>u</mml:mi> <mml:msub> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mrow> <mml:msup> <mml:mi>X</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> <mml:mo>≔</mml:mo> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mrow> <mml:mover> <mml:mi>u</mml:mi> <mml:mo stretchy=\"false\">^</mml:mo> </mml:mover> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>τ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ξ</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo fence=\"false\" stretchy=\"false\">⟨</mml:mo> <mml:mi>ξ</mml:mi> <mml:msup> <mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo> <mml:mi>s</mml:mi> </mml:msup> <mml:mo fence=\"false\" stretchy=\"false\">⟨</mml:mo> <mml:mi>τ</mml:mi> <mml:mo>+</mml:mo> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>ξ</mml:mi> <mml:msup> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <m","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744657","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":"Nikishin’s theorem and factorization through Marcinkiewicz spaces","authors":"Mieczysław Mastyło, Enrique Sánchez Pérez","doi":"10.1090/proc/16888","DOIUrl":"https://doi.org/10.1090/proc/16888","url":null,"abstract":"<p>Consider <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 0\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\"> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding=\"application/x-tex\">F</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-space of all equivalence classes of measurable functions on a finite measure space equipped with the topology of convergence in measure. Inspired by Nikishin’s classical result on the factorization of sublinear continuous operators from a Banach space to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 0\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we prove a theorem that characterizes those maps from any quasi-metric space into <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 0\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> that factor strongly through Marcinkiewicz weighted spaces. We show applications to sublinear operators on a certain class of quasi-Banach spaces with generalized Rademacher type generated by Orlicz sequence spaces.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945161","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":"A remark on a paper by F. Chiarenza and M. Frasca","authors":"N. Krylov","doi":"10.1090/proc/16885","DOIUrl":"https://doi.org/10.1090/proc/16885","url":null,"abstract":"<p>In 1990 F. Chiarenza and M. Frasca published a paper in which they generalized a result of C. Fefferman on estimates of the integral of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartAbsoluteValue b u EndAbsoluteValue Superscript p\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>b</mml:mi> <mml:mi>u</mml:mi> <mml:msup> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">|bu|^{p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> through the integral of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartAbsoluteValue upper D u EndAbsoluteValue Superscript p\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>D</mml:mi> <mml:mi>u</mml:mi> <mml:msup> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">|Du|^{p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p greater-than 1\"> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">p&gt;1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Formally their proof is valid only for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d greater-than-or-equal-to 3\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">dgeq 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We present here further generalization with a different proof in which <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper D\"> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding=\"application/x-tex\">D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is replaced with the fractional power of the Laplacian for any dimension <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d greater-than-or-equal-to 2\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">dgeq 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197124","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":"On Pólya’s random walk constants","authors":"Robert Gaunt, Saralees Nadarajah, Tibor Pogány","doi":"10.1090/proc/16854","DOIUrl":"https://doi.org/10.1090/proc/16854","url":null,"abstract":"<p>A celebrated result in probability theory is that a simple symmetric random walk on the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d\"> <mml:semantics> <mml:mi>d</mml:mi> <mml:annotation encoding=\"application/x-tex\">d</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional lattice <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Z Superscript d\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">Z</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {Z}^d</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is recurrent for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d equals 1 comma 2\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">d=1,2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and transient for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d greater-than-or-equal-to 3\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">dgeq 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In this note, we derive a closed-form expression, in terms of the Lauricella function <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F Subscript upper C\"> <mml:semantics> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>C</mml:mi> </mml:msub> <mml:annotation encoding=\"application/x-tex\">F_C</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, for the return probability for all <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d greater-than-or-equal-to 3\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">dgeq 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Previously, a closed-form formula had only been available for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d equals 3\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">d=3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503309","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":"Supersingular curves of genus four in characteristic two","authors":"Dušan Dragutinović","doi":"10.1090/proc/16792","DOIUrl":"https://doi.org/10.1090/proc/16792","url":null,"abstract":"<p>We describe the intersection of the Torelli locus <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"j left-parenthesis script upper M 4 Superscript c t Baseline right-parenthesis equals script upper J 4\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>j</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msubsup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>4</mml:mn>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>c</mml:mi>\u0000 <mml:mi>t</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msubsup>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">J</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>4</mml:mn>\u0000 </mml:msub>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">j(mathcal {M}_4^{ct}) = mathcal {J}_4</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> with Newton and Ekedahl-Oort strata related to the supersingular locus in characteristic 2. We show that the locus of supersingular Jacobians <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper S 4 intersection script upper J 4\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">S</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>4</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo>∩<!-- ∩ --></mml:mo>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">J</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>4</mml:mn>\u0000 </mml:msub>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {S}_4cap mathcal {J}_4</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> in characteristic 2 is pure of dimension three. One way to obtain that result uses an analysis of the data of smooth genus four curves and principally polarized abelian fourfolds defined over <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper F 2\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">F</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {F}_2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, and another involves a more careful study of some relevant Ekedahl-Oort loci.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140712543","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":"Stabilisation of waves on product manifolds by boundary strips","authors":"Ruoyu Wang","doi":"10.1090/proc/16242","DOIUrl":"https://doi.org/10.1090/proc/16242","url":null,"abstract":"<p>We show that a transversely geometrically controlling boundary damping strip is sufficient but not necessary for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"t Superscript negative 1 slash 2\"> <mml:semantics> <mml:msup> <mml:mi>t</mml:mi> <mml:mrow> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">t^{-1/2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-decay of waves on product manifolds. We give a general scheme to turn resolvent estimates for impedance problems on cross-sections to wave decay on product manifolds.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938846","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":"A note on new weighted geometric inequalities for hypersurfaces in ℝⁿ","authors":"Jie Wu","doi":"10.1090/proc/16875","DOIUrl":"https://doi.org/10.1090/proc/16875","url":null,"abstract":"<p>In this note, we prove a family of sharp weighed inequalities which involve weighted <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>-th mean curvature integral and two distinct quermassintegrals for closed hypersurfaces in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper R Superscript n\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {R}^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. This inequality generalizes the corresponding result of Wei and Zhou [Bull. Lond. Math. Soc. 55 (2023), pp. 263–281] where their proof is based on earlier results of Kwong-Miao [Pacific J. Math. 267 (2014), pp. 417–422; Commun. Contemp. Math. 17 (2015), p. 1550014]. Here we present a proof which does not rely on Kwong-Miao’s results.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744655","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}