Advances in Mathematics最新文献

{"title":"Ladders and squares","authors":"Lorenzo Notaro","doi":"10.1016/j.aim.2025.110714","DOIUrl":"10.1016/j.aim.2025.110714","url":null,"abstract":"<div><div>In 1984, Ditor asked two questions:<ul><li><span>(A)</span><span><div>For each <span><math><mi>n</mi><mo>∈</mo><mi>ω</mi></math></span> and infinite cardinal <em>κ</em>, is there a join-semilattice of breadth <span><math><mi>n</mi><mo>+</mo><mn>1</mn></math></span> and cardinality <span><math><msup><mrow><mi>κ</mi></mrow><mrow><mo>+</mo><mi>n</mi></mrow></msup></math></span> whose principal ideals have cardinality &lt;<em>κ</em>?</div></span></li><li><span>(B)</span><span><div>For each <span><math><mi>n</mi><mo>∈</mo><mi>ω</mi></math></span>, is there a lower finite lattice of cardinality <span><math><msub><mrow><mi>ℵ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> whose elements have at most <span><math><mi>n</mi><mo>+</mo><mn>1</mn></math></span> lower covers?</div></span></li></ul> We show that both questions have positive answers under the axiom of constructibility, and hence consistently with <span><math><mi>ZFC</mi></math></span>. More specifically, we derive the positive answers from assuming that <span><math><msub><mrow><mo>□</mo></mrow><mrow><mi>κ</mi></mrow></msub></math></span> holds for enough <em>κ</em>'s.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"485 ","pages":"Article 110714"},"PeriodicalIF":1.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145600402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symplectic fillings of unit cotangent bundles of spheres and applications","authors":"Myeonggi Kwon ,&nbsp;Takahiro Oba","doi":"10.1016/j.aim.2025.110748","DOIUrl":"10.1016/j.aim.2025.110748","url":null,"abstract":"<div><div>We prove the uniqueness, up to diffeomorphism, of symplectically aspherical fillings of the unit cotangent bundle of odd-dimensional spheres. As applications, we first show the non-existence of exact symplectic cobordisms between some 5-dimensional Brieskorn manifolds. We also determine the diffeomorphism types of closed symplectic 6-manifolds with certain codimension 2 symplectic submanifolds.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"486 ","pages":"Article 110748"},"PeriodicalIF":1.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the classification of finite quasi-quantum groups over abelian groups","authors":"Hua-Lin Huang ,&nbsp;Gongxiang Liu ,&nbsp;Yuping Yang ,&nbsp;Yu Ye","doi":"10.1016/j.aim.2025.110740","DOIUrl":"10.1016/j.aim.2025.110740","url":null,"abstract":"<div><div>Using a variety of methods developed in the theory of finite-dimensional quasi-Hopf algebras, we classify all finite-dimensional coradically graded pointed coquasi-Hopf algebras over abelian groups. As a consequence, we partially confirm the generation conjecture of pointed finite tensor categories due to Etingof, Gelaki, Nikshych and Ostrik.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"486 ","pages":"Article 110740"},"PeriodicalIF":1.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145760672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Minkowski problems of centro-section measures","authors":"Xiaxing Cai ,&nbsp;Gangsong Leng ,&nbsp;Yuchi Wu ,&nbsp;Dongmeng Xi","doi":"10.1016/j.aim.2025.110743","DOIUrl":"10.1016/j.aim.2025.110743","url":null,"abstract":"<div><div>In a previous work in affine convex geometry, an affine contravariant family of geometric measures (called <em>affine dual curvature measures</em>) was introduced. In that work, the authors solved a related affine dual Minkowski problem. The new affine family of Minkowski problems includes the logarithmic Minkowski problem as a special case.</div><div>In that spirit, this work introduces a series of geometric measures (called <em>centro-section measures</em>) that are derived from random sections. The centro-section measures serve to unify dual curvature measures and their affine analogs. Additionally, sufficient conditions are offered to solve the even Minkowski problem for the centro-section measures.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"486 ","pages":"Article 110743"},"PeriodicalIF":1.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Almost meromorphic modular forms and their associated L-functions","authors":"Zikang Dong ,&nbsp;Weijia Wang ,&nbsp;Hao Zhang","doi":"10.1016/j.aim.2025.110745","DOIUrl":"10.1016/j.aim.2025.110745","url":null,"abstract":"<div><div>This paper investigates the analytic properties of <em>L</em>-functions associated with almost meromorphic modular forms, extending classical results on <em>L</em>-functions of holomorphic modular forms. By generalizing the regularized Mellin transform, we define these <em>L</em>-functions and examine their properties, especially the distributions of zeros on the critical line. We prove that under certain singularity conditions, these <em>L</em>-functions have infinitely many zeros on the critical line. Additionally, we establish converse theorems for almost meromorphic modular forms, showing that their <em>L</em>-functions uniquely determine the forms. Numerical evidence is also included to support these results.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"486 ","pages":"Article 110745"},"PeriodicalIF":1.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A∞ deformations of extended Khovanov arc algebras and Stroppel's conjecture","authors":"Severin Barmeier ,&nbsp;Zhengfang Wang","doi":"10.1016/j.aim.2025.110733","DOIUrl":"10.1016/j.aim.2025.110733","url":null,"abstract":"<div><div>Extended Khovanov arc algebras <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> are graded associative algebras which naturally appear in a variety of contexts, from knot and link homology, low-dimensional topology and topological quantum field theory to representation theory and symplectic geometry. C. Stroppel conjectured in her ICM 2010 address that the bigraded Hochschild cohomology groups of <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> vanish in a certain range, implying that the algebras <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> admit no nontrivial A_∞ deformations, in particular that the algebras are intrinsically formal.</div><div>Whereas Stroppel's conjecture is known to hold for the algebras <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msubsup></math></span> and <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> by work of Seidel and Thomas, we show that <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> does in fact admit nontrivial A_∞ deformations with nonvanishing higher products for all <span><math><mi>m</mi><mo>,</mo><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>.</div><div>We describe both the extended Khovanov arc algebras <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> and their Koszul duals concretely as path algebras of quivers with relations. This allows us to give an explicit algebraic construction of A_∞ deformations of <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> by using the correspondence between A_∞ deformations of a Koszul algebra and filtered associative deformations of its Koszul dual.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"485 ","pages":"Article 110733"},"PeriodicalIF":1.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145749188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global stability and sharp decay estimates for 3D MHD equations with only vertical dissipation near a background magnetic field","authors":"Suhua Lai ,&nbsp;Jiahong Wu ,&nbsp;Jianwen Zhang ,&nbsp;Xiaokui Zhao","doi":"10.1016/j.aim.2025.110747","DOIUrl":"10.1016/j.aim.2025.110747","url":null,"abstract":"<div><div>This paper is concerned with the stability and large-time behavior of 3D incompressible MHD equations with only vertical dissipation near a background magnetic field. By making full use of the dissipation generated by the background magnetic field, we first establish the global stability of the solutions in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>-norm. Then, the optimal decay rates of the solutions are obtained, which are consistent with the 2D classical heat equation. Moreover, some enhanced decay rates of <span><math><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></math></span> are also achieved. In other words, the decay estimates of the second or third component of velocity/magnetic field coincide with those of 2D heat kernel, while the first component behaves like the 3D heat kernel. This is mainly due to the divergence-free condition and the anisotropic structure.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"486 ","pages":"Article 110747"},"PeriodicalIF":1.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pluriclosed flow and the Hull-Strominger system","authors":"Mario Garcia-Fernandez ,&nbsp;Raul Gonzalez Molina ,&nbsp;Jeffrey Streets","doi":"10.1016/j.aim.2025.110699","DOIUrl":"10.1016/j.aim.2025.110699","url":null,"abstract":"<div><div>We define a natural extension of pluriclosed flow aiming at constructing solutions of the Hull-Strominger system. We give several geometric formulations of this flow, which yield a series of a priori estimates for the flow and also for the Hull-Strominger system. The evolution equations are derived using the theory of string algebroids, a class of Courant algebroids which occur naturally in higher gauge theory. Using this, we interpret the flow as generalized Ricci flow and also as a higher/coupled version of Hermitian-Yang-Mills flow, proving furthermore that it is compatible with symmetry reduction. Regarding analytical results, we prove a priori <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> estimates for uniformly parabolic solutions. This in particular settles the question of smooth regularity of uniformly elliptic solutions of the Hull-Strominger system, generalizing Yau's <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> estimate for the complex Monge-Ampère equation. We prove global existence and convergence results for the flow on special backgrounds, and discuss a conjectural relationship of the flow to the geometrization of Reid's fantasy.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"485 ","pages":"Article 110699"},"PeriodicalIF":1.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145694482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rigidity of saddle loops","authors":"Daniel Panazzolo ,&nbsp;Maja Resman ,&nbsp;Loïc Teyssier","doi":"10.1016/j.aim.2025.110712","DOIUrl":"10.1016/j.aim.2025.110712","url":null,"abstract":"<div><div>A saddle loop is a germ of a holomorphic foliation near a homoclinic saddle connection. We prove that they are classified by their Poincaré first-return map. We also prove that they are formally rigid when the Poincaré map is multivalued. Finally, we provide a list of all analytic classes of Liouville-integrable saddle loops.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"485 ","pages":"Article 110712"},"PeriodicalIF":1.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145749191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Serrin-type over-determined problem for Hessian equations in the exterior domain","authors":"Bo Wang ,&nbsp;Zhizhang Wang","doi":"10.1016/j.aim.2025.110737","DOIUrl":"10.1016/j.aim.2025.110737","url":null,"abstract":"<div><div>In this paper, we consider the Hessian equations in some exterior domain with prescribed asymptotic behavior at infinity and Dirichlet-Neumann conditions on its interior boundary. We obtain that there exists a unique bounded domain such that the over-determined problem admits a unique strictly convex solution.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"485 ","pages":"Article 110737"},"PeriodicalIF":1.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}