{"title":"A priori estimates for negative constant scalar curvature conformal metrics with positive constant boundary mean curvature","authors":"Sérgio Almaraz, 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":"Matrix-weighted Besov-type and Triebel–Lizorkin-type spaces II: Sharp boundedness of almost diagonal operators","authors":"Fan Bu, Tuomas Hytönen, Dachun Yang, 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, Martin Kalck, 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, 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, Yuri Tschinkel, 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}