Advances in Mathematics最新文献

{"title":"Deformations of homotopy theories via algebraic theories","authors":"William Balderrama","doi":"10.1016/j.aim.2025.110496","DOIUrl":"10.1016/j.aim.2025.110496","url":null,"abstract":"<div><div>We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral sequences that compute homotopical data starting with purely algebraic data.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110496"},"PeriodicalIF":1.5,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144907158","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":"Odd unimodal sequences","authors":"Kathrin Bringmann ,&nbsp;Jeremy Lovejoy","doi":"10.1016/j.aim.2025.110458","DOIUrl":"10.1016/j.aim.2025.110458","url":null,"abstract":"<div><div>In this paper we study odd unimodal and odd strongly unimodal sequences. We use <em>q</em>-series methods to find several fundamental generating functions. Employing the Euler–Maclaurin summation formula we obtain the asymptotic main term for both types of sequences. We also find families of congruences modulo 4 for the number of odd strongly unimodal sequences.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110458"},"PeriodicalIF":1.5,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144903965","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 general Heegaard Floer surgery formula","authors":"Ian Zemke","doi":"10.1016/j.aim.2025.110489","DOIUrl":"10.1016/j.aim.2025.110489","url":null,"abstract":"<div><div>We give several new perspectives on the Heegaard Floer Dehn surgery formulas of Manolescu, Ozsváth and Szabó. Our main result is a new exact triangle in the Fukaya category of the torus which gives a new proof of these formulas. This exact triangle is different from the one which appeared in Ozsváth and Szabó's original proof. This exact triangle simplifies a number of technical aspects in their proofs and also allows us to prove several new results. A first application is an extension of the link surgery formula to arbitrary links in closed 3-manifolds, with no restrictions on the link being null-homologous. A second application is a proof that the modules for bordered manifolds with torus boundaries, defined by the author in a previous paper, are invariants. Another application is a simple proof of a version of the surgery formula which computes knot and link Floer complexes in terms of subcubes of the link surgery hypercube. As a final application, we show that the knot surgery algebra is homotopy equivalent to an endomorphism algebra of a sum of two decorated Lagrangians in the torus, mirroring a result of Auroux concerning the algebras of Lipshitz, Ozsváth and Thurston.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110489"},"PeriodicalIF":1.5,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895677","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":"Finite-time singularity via multi-layer degenerate pendula for the 2D Boussinesq equation with uniform C1,43−1−ε∩L2 force","authors":"Diego Córdoba ,&nbsp;Andrés Laín-Sanclemente ,&nbsp;Luis Martínez-Zoroa","doi":"10.1016/j.aim.2025.110480","DOIUrl":"10.1016/j.aim.2025.110480","url":null,"abstract":"<div><div>We establish the existence of compactly supported solutions of the inviscid incompressible 2D Boussinesq equation with <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><msqrt><mrow><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msqrt><mo>−</mo><mn>1</mn><mo>−</mo><mi>ε</mi></mrow></msup><mo>∩</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> force that develop a singularity in finite time. Importantly, the force preserves this regularity at the blow-up time. Moreover, the forces in the vorticity and density equations have compact support. The mechanism behind the blow-up is an accumulated hysteresis effect on the vorticity caused by an infinite chain of “degenerate” pendula and flickering density.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110480"},"PeriodicalIF":1.5,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893528","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":"The algebraic degree of coupled oscillators","authors":"Paul Breiding ,&nbsp;Mateusz Michałek ,&nbsp;Leonid Monin ,&nbsp;Simon Telen","doi":"10.1016/j.aim.2025.110492","DOIUrl":"10.1016/j.aim.2025.110492","url":null,"abstract":"<div><div>Approximating periodic solutions to the coupled Duffing equations amounts to solving a system of polynomial equations. The number of complex solutions measures the algebraic complexity of this approximation problem. Using the theory of Khovanskii bases, we show that this number is given by the volume of a polytope. We also show how to compute all solutions using numerical nonlinear algebra.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110492"},"PeriodicalIF":1.5,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144885484","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":"C2 estimates for k-Hessian equations and a rigidity theorem","authors":"Ruijia Zhang","doi":"10.1016/j.aim.2025.110488","DOIUrl":"10.1016/j.aim.2025.110488","url":null,"abstract":"<div><div>We derive a concavity inequality for <em>k</em>-Hessian operators under the semiconvexity condition. As an application, we establish interior estimates for semiconvex solutions to the <em>k</em>-Hessian equations with vanishing Dirichlet boundary conditions and obtain a Liouville-type result. This result confirms Chang-Yuan's conjecture [4] under the super quadratic growth condition.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110488"},"PeriodicalIF":1.5,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144887277","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":"Sharp Beckner's inequalities for axially symmetric functions on S6 and S8","authors":"Changfeng Gui ,&nbsp;Tuoxin Li ,&nbsp;Juncheng Wei ,&nbsp;Zikai Ye","doi":"10.1016/j.aim.2025.110487","DOIUrl":"10.1016/j.aim.2025.110487","url":null,"abstract":"<div><div>We prove that for <span><math><mi>N</mi><mo>=</mo><mn>6</mn></math></span> and 8, axially symmetric solutions to the <em>Q</em>-curvature type problem<span><span><span><math><mi>α</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>N</mi></mrow></msub><mi>u</mi><mo>+</mo><mo>(</mo><mi>N</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>!</mo><mo>(</mo><mn>1</mn><mo>−</mo><mfrac><mrow><msup><mrow><mi>e</mi></mrow><mrow><mi>N</mi><mi>u</mi></mrow></msup></mrow><mrow><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>S</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></msub><msup><mrow><mi>e</mi></mrow><mrow><mi>N</mi><mi>u</mi></mrow></msup></mrow></mfrac><mo>)</mo><mo>=</mo><mn>0</mn><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mtext>on</mtext><mspace></mspace><msup><mrow><mi>S</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span></span></span> must be constants, provided that <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>≤</mo><mi>α</mi><mo>&lt;</mo><mn>1</mn></math></span> and the center of mass of <em>u</em> is at the origin. We also show that this result is sharp. This result closes the gap of the related results in <span><span>[21]</span></span>, which proved a similar uniqueness result for <span><math><mi>α</mi><mo>≥</mo><mn>0.6168</mn></math></span> when <span><math><mi>N</mi><mo>=</mo><mn>6</mn></math></span> and <span><math><mi>α</mi><mo>≥</mo><mn>0.8261</mn></math></span> when <span><math><mi>N</mi><mo>=</mo><mn>8</mn></math></span>. As a consequence, we attain the best constant of sharp Beckner's inequality for axially symmetric functions on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>6</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>8</mn></mrow></msup></math></span> whose center of mass is at the origin and answer the generalized Chang-Yang conjecture positively in the axially symmetric case when <span><math><mi>N</mi><mo>=</mo><mn>6</mn></math></span> and <span><math><mi>N</mi><mo>=</mo><mn>8</mn></math></span>. The improvement is based on two types of new estimates. One is the refined estimate of the semi-norm <span><math><msup><mrow><mo>⌊</mo><mi>G</mi><mo>⌋</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> using a new way of integration by parts. The other is a family of refined pointwise estimates (<span><span>Lemma 3.7</span></span>, <span><span>Lemma 3.9</span></span>) on Gegenbauer coefficients, which is established by the decaying estimates and cancellation property of Gegenbauer polynomials (<span><span>Lemma 3.10</span></span>, <span><span>Proposition 3.11</span></span>, <span><span>Corollary 3.12</span></span>). In particular, we use a three-fold line function when <span><math><mi>N</mi><mo>=</mo><mn>8</mn></math></span> to further enhance the estimates of Gegenbauer polynomials.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110487"},"PeriodicalIF":1.5,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144879404","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":"Stable cohomology of Aut(Fn) with bivariant twisted coefficients","authors":"Erik Lindell","doi":"10.1016/j.aim.2025.110483","DOIUrl":"10.1016/j.aim.2025.110483","url":null,"abstract":"<div><div>We compute the cohomology groups of the automorphism group of the free group <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, with coefficients in arbitrary tensor products of the standard rational representation <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><mi>Q</mi><mo>)</mo></math></span> and its dual, in a range where <em>n</em> is sufficiently large compared to the cohomological degree and the number of tensor factors.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110483"},"PeriodicalIF":1.5,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144879403","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":"Hypersurfaces of constant scalar curvature in hyperbolic space with prescribed asymptotic boundary at infinity","authors":"Bin Wang","doi":"10.1016/j.aim.2025.110493","DOIUrl":"10.1016/j.aim.2025.110493","url":null,"abstract":"<div><div>This article concerns a natural generalization of the classical asymptotic Plateau problem in hyperbolic space. We prove the existence of a smooth complete hypersurface of constant scalar curvature with a prescribed asymptotic boundary at infinity. The desired hypersurface is constructed as the limit of constant scalar curvature graphs (with respect to vertical geodesics) over a fixed compact domain in a horosphere, and the problem is thus reduced to solving a Dirichlet problem for a fully nonlinear elliptic partial differential equation which is degenerate along the boundary. Previously, the result was known only for a restricted range of curvature values. Now, in this article, by introducing some new techniques, we are able to solve the Dirichlet problem for all possible curvature values. The main ingredient is the establishment of the crucial second order a priori estimates for admissible solutions.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110493"},"PeriodicalIF":1.5,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144879402","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":"The Nadler-Quinn problem on accessible points of arc-like continua","authors":"Andrea Ammerlaan ,&nbsp;Ana Anušić ,&nbsp;Logan C. Hoehn","doi":"10.1016/j.aim.2025.110491","DOIUrl":"10.1016/j.aim.2025.110491","url":null,"abstract":"<div><div>We show that if <em>X</em> is an arc-like continuum, then for every point <span><math><mi>x</mi><mo>∈</mo><mi>X</mi></math></span> there is a plane embedding of <em>X</em> in which <em>x</em> is an accessible point. This answers a question posed by Sam B. Nadler in 1972, which has become known as the Nadler-Quinn problem in continuum theory. Towards this end, we develop the theories of truncations and contour factorizations of interval maps. As a corollary, we answer a question of J.C. Mayer from 1982 about inequivalent plane embeddings of indecomposable arc-like continua.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110491"},"PeriodicalIF":1.5,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144863886","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}