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

{"title":"A priori estimates for negative constant scalar curvature conformal metrics with positive constant boundary mean curvature","authors":"Sérgio Almaraz,&nbsp;Shaodong Wang","doi":"10.1112/jlms.70109","DOIUrl":"https://doi.org/10.1112/jlms.70109","url":null,"abstract":"<p>On a compact Riemannian manifold with boundary, we study the set of conformal metrics of negative constant scalar curvature in the interior and positive constant mean curvature on the boundary. Working in the case of positive Yamabe conformal invariant, we prove that this set is a priori bounded in the three-dimensional case and in the locally conformally flat with umbilical boundary case in any dimension not less than three.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513564","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":"Willmore-type inequality in unbounded convex sets","authors":"Xiaohan Jia,&nbsp;Guofang Wang,&nbsp;Chao Xia,&nbsp;Xuwen Zhang","doi":"10.1112/jlms.70105","DOIUrl":"https://doi.org/10.1112/jlms.70105","url":null,"abstract":"<p>In this paper, we prove the following Willmore-type inequality: on an unbounded closed convex set <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <mo>⊂</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$Ksubset mathbb {R}^{n+1}$</annotation>\u0000 </semantics></math> <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$(ngeqslant 2$</annotation>\u0000 </semantics></math>), for any embedded hypersurface <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Σ</mi>\u0000 <mo>⊂</mo>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 <annotation>${Sigma }subset K$</annotation>\u0000 </semantics></math> with boundary <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 <mi>Σ</mi>\u0000 <mo>⊂</mo>\u0000 <mi>∂</mi>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 <annotation>$partial {Sigma }subset partial K$</annotation>\u0000 </semantics></math> satisfying a certain contact angle condition, there holds\u0000\u0000 </p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70105","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513627","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":"Matrix-weighted Besov-type and Triebel–Lizorkin-type spaces II: Sharp boundedness of almost diagonal operators","authors":"Fan Bu,&nbsp;Tuomas Hytönen,&nbsp;Dachun Yang,&nbsp;Wen Yuan","doi":"10.1112/jlms.70094","DOIUrl":"https://doi.org/10.1112/jlms.70094","url":null,"abstract":"<p>This article is the second one of three successive articles of the authors on the matrix-weighted Besov-type and Triebel–Lizorkin-type spaces. In this article, we obtain the sharp boundedness of almost diagonal operators on matrix-weighted Besov-type and Triebel–Lizorkin-type sequence spaces. These results not only possess broad generality but also improve several existing related results in various special cases covered by this family of spaces. This improvement depends, on the one hand, on the notion of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$A_p$</annotation>\u0000 </semantics></math>-dimensions of matrix weights and their properties introduced in the first article of this series and, on the other hand, on a careful direct analysis of sequences of averages avoiding maximal operators. While a recent matrix-weighted extension of the Fefferman–Stein vector-valued maximal inequality would provide an alternative route to some of our results in the restricted range of function space parameters <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mi>q</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$p,qin (1,infty)$</annotation>\u0000 </semantics></math>, our approach covers the full scale of exponents <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$pin (0,infty)$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$qin (0,infty]$</annotation>\u0000 </semantics></math> that is relevant in the theory of function spaces.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143497187","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":"Cluster categories for completed infinity-gons I: Categorifying triangulations","authors":"İlke Çanakçı,&nbsp;Martin Kalck,&nbsp;Matthew Pressland","doi":"10.1112/jlms.70092","DOIUrl":"https://doi.org/10.1112/jlms.70092","url":null,"abstract":"<p>Paquette and Yıldırım recently introduced triangulated categories of arcs in completed infinity-gons, which are discs with an infinite closed set of marked points on their boundary. These categories have many features in common with the cluster categories associated to discs with different sets of marked points. In particular, they have (weak) cluster-tilting subcategories, which Paquette–Yıldırım show are in bijection with very special triangulations of the disc. This is in contrast to Igusa–Todorov's earlier work in the uncompleted case, in which every triangulation corresponds to a weak cluster-tilting subcategory. In this paper, we replace the triangulated structure of Paquette–Yıldırım's category by an extriangulated substructure and prove that, with this structure, the weak cluster-tilting subcategories are once again in bijection with triangulations. We further show that functorial finiteness of a weak cluster-tilting subcategory is equivalent to a very mild condition on the triangulation, which also appears in Çanakçı and Felikson's study of infinite rank cluster algebras from Teichmüller theory. By comparison with the combinatorics of triangulations, we are also able to characterise when weak cluster-tilting subcategories can be mutated in this new extriangulated category.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70092","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143475707","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":"The symplectic density property for Calogero–Moser spaces","authors":"Rafael B. Andrist,&nbsp;Gaofeng Huang","doi":"10.1112/jlms.70100","DOIUrl":"https://doi.org/10.1112/jlms.70100","url":null,"abstract":"<p>We introduce the symplectic density property and the Hamiltonian density property together with the corresponding versions of Andersén–Lempert theory. We establish these properties for the Calogero–Moser space <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>$mathcal {C}_n$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> particles and describe its group of holomorphic symplectic automorphisms.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70100","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143475349","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":"Rationality of forms of \u0000 \u0000 \u0000 \u0000 M\u0000 ¯\u0000 \u0000 \u0000 0\u0000 ,\u0000 n\u0000 \u0000 \u0000 $overline{{mathcal {M}}}_{0,n}$","authors":"Brendan Hassett,&nbsp;Yuri Tschinkel,&nbsp;Zhijia Zhang","doi":"10.1112/jlms.70097","DOIUrl":"https://doi.org/10.1112/jlms.70097","url":null,"abstract":"<p>We study equivariant geometry and rationality of moduli spaces of points on the projective line, for twists associated with permutations of the points.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143466109","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":"Global well-posedness of the variable-order fractional wave equation with variable exponent nonlinearity","authors":"Qiang Lin,&nbsp;Runzhang Xu","doi":"10.1112/jlms.70091","DOIUrl":"https://doi.org/10.1112/jlms.70091","url":null,"abstract":"<p>In this paper, we conduct a comprehensive study of the global well-posedness of solution for a class of nonlocal wave equations with variable-order fractional Laplacian and variable exponent nonlinearity by constructing a suitable framework of the variational theory. We first prove the local-in-time existence of the weak solution via the Galerkin approximation technique and fixed point theory. Then by constructing the potential well theory, we classify the initial data leading to the global existence and finite time blowup of the solution for three different initial energy cases, that is, subcritical initial energy case, critical initial energy case, and supercritical initial energy case. For the subcritical and critical initial energy cases, we show that the solution exists globally in time when the initial data belong to the stable manifold and blows up in finite time when the initial data belong to the unstable manifold. For the supercritical initial energy case, we observe some initial conditions that enable the finite time blow-up solution by an adapted concavity method, and the issue of global existence still remains unsolved. As a further study of finite time blowup, we estimate the upper and lower bounds of blow-up time by using different strategies, that is, applying some first-order differential inequality regardless of the different initial energy levels, to give a unified expression for the lower bound estimation for three initial energy levels. For the upper bound estimation, we utilize two second-order differential inequalities influenced by the different energy levels to give the upper bound estimations of the blow-up time at each initial energy level.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143466111","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":"Weak quasi-\u0000 \u0000 F\u0000 $F$\u0000 -splitting and del Pezzo varieties","authors":"Tatsuro Kawakami,&nbsp;Hiromu Tanaka","doi":"10.1112/jlms.70098","DOIUrl":"https://doi.org/10.1112/jlms.70098","url":null,"abstract":"<p>We show that smooth del Pezzo varieties in positive characteristic are quasi-<span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-split. To this end, we introduce weak quasi-<span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-splitting and we prove that general ladders of smooth del Pezzo varieties are normal.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143466110","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":"Existence of weak solutions and long-time asymptotics for hydrodynamic model of swarming","authors":"Nilasis Chaudhuri,&nbsp;Young-Pil Choi,&nbsp;Oliver Tse,&nbsp;Ewelina Zatorska","doi":"10.1112/jlms.70088","DOIUrl":"https://doi.org/10.1112/jlms.70088","url":null,"abstract":"<p>We consider a one-dimensional hydrodynamic model featuring nonlocal attraction–repulsion interactions and singular velocity alignment. We introduce a two-velocity reformulation and the corresponding energy-type inequality, in the spirit of the Bresch–Desjardins estimate. We identify a dependence between the communication weight and interaction kernel and between the pressure and viscosity term allowing for this inequality to be uniform in time. It is then used to study long-time asymptotics of solutions.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455728","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":"Ground states for aggregation–diffusion models on Cartan–Hadamard manifolds","authors":"Razvan C. Fetecau,&nbsp;Hansol Park","doi":"10.1112/jlms.70079","DOIUrl":"https://doi.org/10.1112/jlms.70079","url":null,"abstract":"<p>We consider a free energy functional on Cartan–Hadamard manifolds and investigate the existence of its global minimizers. The energy functional consists of two components: an entropy (or internal energy) and an interaction energy modelled by an attractive potential. The two components have competing effects, as they favour spreading by linear diffusion and blow-up by non-local attractive interactions, respectively. We find necessary and sufficient conditions for ground states to exist, in terms of the behaviours of the attractive potential at infinity and at zero. In particular, for general Cartan–Hadamard manifolds, <i>superlinear</i> growth at infinity of the attractive potential prevents the spreading. The behaviour can be relaxed for homogeneous manifolds, for which only <i>linear</i> growth of the potential is sufficient for this purpose. As a key tool in our analysis, we develop a new logarithmic Hardy–Littlewood–Sobolev inequality on Cartan–Hadamard manifolds.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455788","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}