Journal of the London Mathematical Society-Second Series最新文献

{"title":"Generalising Collins' theorem","authors":"James Howie,&nbsp;Hamish Short","doi":"10.1112/jlms.70240","DOIUrl":"10.1112/jlms.70240","url":null,"abstract":"<p>We generalise a result of D. J. Collins on intersections of conjugates of Magnus subgroups of one-relator groups to the context of one-relator products of locally indicable groups.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70240","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Supersonic flows of the Euler–Poisson system with nonzero vorticities in three-dimensional cylinders","authors":"Myoungjean Bae,&nbsp;Hyangdong Park","doi":"10.1112/jlms.70233","DOIUrl":"10.1112/jlms.70233","url":null,"abstract":"<p>We prove the unique existence of three-dimensional supersonic solutions to the steady Euler–Poisson system in cylindrical nozzles. First, we establish the unique existence of irrotational solutions in a cylindrical nozzle with an arbitrary cross-section with using weighted Sobolev norms. Then, we establish the unique existence of axisymmetric solutions with nonzero vorticity in a circular cylinder. Several technical issues, including the issue of nonlinear hyperbolic–elliptic mixed type partial differential equation (PDE) system and corner singularities in a Lipschitz domain, are carefully addressed.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70233","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Peculiar behavior of the principal Laplacian eigenvalue for large negative Robin parameters","authors":"Charlotte Dietze,&nbsp;Konstantin Pankrashkin","doi":"10.1112/jlms.70242","DOIUrl":"10.1112/jlms.70242","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;⊂&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Omega subset mathbb {R}^n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$ngeqslant 2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a bounded Lipschitz domain with outer unit normal &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ν&lt;/mi&gt;\u0000 &lt;annotation&gt;$nu$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. For &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$alpha in mathbb {R}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;annotation&gt;$R_Omega ^alpha$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be the Laplacian in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;annotation&gt;$Omega$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with the Robin boundary condition &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;ν&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$partial _nu u+alpha u=0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and denote by &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$E(R^alpha _Omega)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; its principal eigenvalue. In 2017, Bucur, Freitas, and Kennedy stated the following open question: &lt;i&gt;Does the limit of the ratio&lt;/i&gt; &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70242","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite generation of \u0000 \u0000 \u0000 split-\u0000 F\u0000 -regular\u0000 \u0000 $text{split-}Ftext{-regular}$\u0000 monoid algebras","authors":"Rankeya Datta,&nbsp;Karl Schwede,&nbsp;Kevin Tucker","doi":"10.1112/jlms.70234","DOIUrl":"10.1112/jlms.70234","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;annotation&gt;$S$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a submonoid of a free Abelian group of finite rank. We show that if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;annotation&gt;$k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a field of prime characteristic such that the monoid &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;annotation&gt;$k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-algebra &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$k[S]$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtext&gt;split-&lt;/mtext&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mtext&gt;-regular&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$text{split-}Ftext{-regular}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, then &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$k[S]$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a finitely generated &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;annotation&gt;$k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-algebra, or equivalently, that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;annotation&gt;$S$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a finitely generated monoid. Split-&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-regular rings are possibly non-Noetherian or non-&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-finite rings that satisfy the defining property of strongly &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-regular rings from the theories of tight closure and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-singularities. Our finite generation result provides evidence in favor of the conjecture that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtext&gt;split-&lt;/mtext&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mtext&gt;-regular&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$text{split-}Ftext{-regular}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; rings in funct","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681160","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":"Discrete Laplacians — Spherical and hyperbolic","authors":"Ivan Izmestiev,&nbsp;Wai Yeung Lam","doi":"10.1112/jlms.70235","DOIUrl":"10.1112/jlms.70235","url":null,"abstract":"<p>The discrete Laplacian on Euclidean triangulated surfaces is a well-established notion. We introduce discrete Laplacians on spherical and hyperbolic triangulated surfaces. On the one hand, our definitions are close to the Euclidean one in that the edge weights contain the cotangents of certain combinations of angles and are non-negative if and only if the triangulation is Delaunay. On the other hand, these discretizations are structure-preserving in several respects. We prove that the area of a convex polyhedron can be written in terms of the discrete spherical Laplacian of the support function, whose expression is the same as the area of a smooth convex body in terms of the usual spherical Laplacian. We show that the conformal factors of discrete conformal vector fields on a triangulated surface of curvature <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>∈</mo>\u0000 <mo>{</mo>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$k in lbrace -1,1rbrace$</annotation>\u0000 </semantics></math> are <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation>$-2k$</annotation>\u0000 </semantics></math>-eigenfunctions of our discrete Laplacians, exactly as in the smooth setting. The discrete conformality can be understood here both in the sense of the vertex scaling and in the sense of circle patterns. Finally, we connect the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation>$-2k$</annotation>\u0000 </semantics></math>-eigenfunctions to infinitesimal isometric deformations of a polyhedron inscribed into corresponding quadrics.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681158","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":"The combined singular limits of compressible Oldroyd-B model at low Mach and Weissenberg numbers","authors":"Jianwen Zhang,&nbsp;Minghui Zhong","doi":"10.1112/jlms.70243","DOIUrl":"10.1112/jlms.70243","url":null,"abstract":"<p>This paper is concerned with an initial-boundary value problem of the compressible Oldroyd-B (OB) model on 3D bounded and smooth domain subject to Navier's slip boundary conditions. The combined singular limits at low Mach and Weissenberg numbers are justified for the global smooth solutions with ill-prepared initial data and non-small coupling parameter. It is shown that as the Mach number and the Weissenberg number tend to zero, the solution of the compressible OB model for viscoelastic fluids converges to that of the incompressible Navier–Stokes equations for Newtonian fluids. The proofs are based on some subtle weighted estimates in Sobolev spaces. The different weights of various norms need to be chosen carefully such that the large singular operators can be well balanced and the linear interactions between the deformation and the divergence of extra stress tensor can be mutually cancelled.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681244","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":"The De Giorgi method for local and nonlocal systems","authors":"Linus Behn,&nbsp;Lars Diening,&nbsp;Simon Nowak,&nbsp;Toni Scharle","doi":"10.1112/jlms.70237","DOIUrl":"10.1112/jlms.70237","url":null,"abstract":"<p>We extend the De Giorgi iteration technique to the vectorial setting. For this we replace the usual scalar truncation operator by a vectorial shortening operator. As an application, we prove local boundedness for local and nonlocal nonlinear systems. Furthermore, we show convex hull properties, which are a generalization of the maximum principle to the case of systems.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70237","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the dimension of orthogonal projections of self-similar measures","authors":"Amir Algom,&nbsp;Pablo Shmerkin","doi":"10.1112/jlms.70245","DOIUrl":"10.1112/jlms.70245","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>ν</mi>\u0000 <annotation>$nu$</annotation>\u0000 </semantics></math> be a self-similar measure on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^d$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$dgeqslant 2$</annotation>\u0000 </semantics></math>, and let <span></span><math>\u0000 <semantics>\u0000 <mi>π</mi>\u0000 <annotation>$pi$</annotation>\u0000 </semantics></math> be an orthogonal projection onto a <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>-dimensional subspace. We formulate a criterion on the action of the group generated by the orthogonal parts of the iterated function system on <span></span><math>\u0000 <semantics>\u0000 <mi>π</mi>\u0000 <annotation>$pi$</annotation>\u0000 </semantics></math>, and show that it ensures that the dimension of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>π</mi>\u0000 <mi>ν</mi>\u0000 </mrow>\u0000 <annotation>$pi nu$</annotation>\u0000 </semantics></math> is preserved; this significantly refines previous results by Hochman–Shmerkin (2012) and Falconer–Jin (2014), and is sharp for projections to lines and hyperplanes. A key ingredient in the proof is an application of a restricted projection theorem of Gan–Guo–Wang (2024).</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70245","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the one-dimensional polynomial, regular, and regulous images of closed balls and spheres","authors":"José F. Fernando","doi":"10.1112/jlms.70241","DOIUrl":"10.1112/jlms.70241","url":null,"abstract":"&lt;p&gt;We present a full geometric characterization of the one-dimensional (semialgebraic) images &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;annotation&gt;$S$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of either &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;annotation&gt;$n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-dimensional closed balls &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mover&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mo&gt;¯&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;⊂&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$overline{{mathcal {B}}}_nsubset {mathbb {R}}^n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; or &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;annotation&gt;$n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-dimensional spheres &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;⊂&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${mathbb {S}}^nsubset {mathbb {R}}^{n+1}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; under polynomial, regular, and regulous maps for some &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$ngeqslant 1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In all the previous cases, one can find a new polynomial, regular, or regulous map with domain either &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mover&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mo&gt;¯&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70241","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144666434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some applications of abelianization in Gromov–Witten theory","authors":"Nawaz Sultani,&nbsp;Rachel Webb","doi":"10.1112/jlms.70236","DOIUrl":"10.1112/jlms.70236","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> be a complex reductive group and let <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$E$</annotation>\u0000 </semantics></math> be two linear representations of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>. Let <span></span><math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$Y$</annotation>\u0000 </semantics></math> be a complete intersection in <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> equal to the zero locus of a <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-equivariant section of the trivial bundle <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 <mo>×</mo>\u0000 <mi>X</mi>\u0000 <mo>→</mo>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 <annotation>$E times X rightarrow X$</annotation>\u0000 </semantics></math>. We explain some general techniques for using quasimap formulas to compute useful <span></span><math>\u0000 <semantics>\u0000 <mi>I</mi>\u0000 <annotation>$I$</annotation>\u0000 </semantics></math>-functions of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Y</mi>\u0000 <mrow>\u0000 <mo>/</mo>\u0000 <mo>/</mo>\u0000 </mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation>$Ymathord {/hspace{-3.33328pt}/}G$</annotation>\u0000 </semantics></math>. We work several explicit examples, including a rigorous derivation of the conjectural quantum period in Oneto and Petracci (Adv. Geom. <b>18</b> (2018), no. 3, 303–336).</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144647281","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}