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

{"title":"Log-BMO matrix weights and quasilinear elliptic equations with Orlicz growth in Reifenberg domains","authors":"Sun-Sig Byun,&nbsp;Rui Yang","doi":"10.1112/jlms.70151","DOIUrl":"https://doi.org/10.1112/jlms.70151","url":null,"abstract":"<p>We study a very general quasilinear elliptic equation with the nonlinearity with Orlicz growth subject to a degenerate or singular matrix weight on a bounded nonsmooth domain. The nonlinearity satisfies a nonstandard growth condition related to the associated Young function, and the logarithm of the matrix weight in BMO (bounded mean oscillation) is constrained by a smallness parameter which has a close relationship with the Young function. We establish a global Calderón–Zygmund estimate for the weak solution of such a degenerate or singular problem in the setting of a weighted Orlicz space under a minimal geometric assumption that the boundary of the domain is sufficiently flat in the Reifenberg sense. Our regularity result is, up to our knowledge, the first one available for divergence structure quasilinear elliptic equations with matrix weights and nonstandard growth in the literature.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809493","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":"On a common refinement of Stark units and Gross–Stark units","authors":"Tomokazu Kashio","doi":"10.1112/jlms.70147","DOIUrl":"https://doi.org/10.1112/jlms.70147","url":null,"abstract":"<p>The purpose of this paper is to formulate and study a common refinement of a version of Stark's conjecture and its <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-adic analogue, in terms of Fontaine's <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-adic period ring. We construct period-ring-valued functions under a generalization of Yoshida's conjecture on the transcendental parts of CM-periods. Then, we formulate a conjecture on the reciprocity law on their special values concerning the absolute Frobenius action. We show that our conjecture implies a part of Stark's conjecture when the base field is an arbitrary real field and the splitting place is a real place. It also implies a refinement of the Gross–Stark conjecture under a certain assumption. When the base field is the rational number field, we see that our conjecture follows from Coleman's formula on Fermat curves. We also provide some partial results in other cases.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70147","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809490","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":"Marked length spectrum rigidity in groups with contracting elements","authors":"Renxing Wan,&nbsp;Xiaoyu Xu,&nbsp;Wenyuan Yang","doi":"10.1112/jlms.70146","DOIUrl":"https://doi.org/10.1112/jlms.70146","url":null,"abstract":"<p>This paper presents a study of the well-known marked length spectrum rigidity problem in the coarse-geometric setting. For any two (possibly non-proper) group actions <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mi>↷</mi>\u0000 <msub>\u0000 <mi>X</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$Gcurvearrowright X_1$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mi>↷</mi>\u0000 <msub>\u0000 <mi>X</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$Gcurvearrowright X_2$</annotation>\u0000 </semantics></math> with contracting property, we prove that if the two actions have the same marked length spectrum, then the orbit map <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <msub>\u0000 <mi>o</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>→</mo>\u0000 <mi>G</mi>\u0000 <msub>\u0000 <mi>o</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$Go_1rightarrow Go_2$</annotation>\u0000 </semantics></math> must be a rough isometry. In the special case of cusp-uniform actions, the rough isometry can be extended to the entire space. This generalises the existing results in hyperbolic groups and relatively hyperbolic groups. In addition, we prove a finer marked length spectrum rigidity from confined subgroups and further, geometrically dense subgroups. Our proof is based on the Extension Lemma and uses purely elementary metric geometry. This study produces new results and recovers existing ones for many more interesting groups through a unified and elementary approach.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809492","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":"New building blocks for \u0000 \u0000 \u0000 F\u0000 1\u0000 \u0000 ${mathbb {F}}_1$\u0000 -geometry: Bands and band schemes","authors":"Matthew Baker,&nbsp;Tong Jin,&nbsp;Oliver Lorscheid","doi":"10.1112/jlms.70125","DOIUrl":"https://doi.org/10.1112/jlms.70125","url":null,"abstract":"<p>We develop and study a generalization of commutative rings called <i>bands</i>, along with the corresponding geometric theory of <i>band schemes</i>. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle. They form a ring-like counterpart to the field-like category of <i>idylls</i> introduced by the first and third authors in the previous work. The first part of the paper is dedicated to establishing fundamental properties of bands analogous to basic facts in commutative algebra. In particular, we introduce various kinds of ideals in a band and explore their properties, and we study localization, quotients, limits, and colimits. The second part of the paper studies band schemes. After giving the definition, we present some examples of band schemes, along with basic properties of band schemes and morphisms thereof, and we describe functors into some other scheme theories. In the third part, we discuss some “visualizations” of band schemes, which are different topological spaces that one can functorially associate to a band scheme <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70125","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793524","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":"Quantum automorphism groups of lexicographic products of graphs","authors":"Arnbjörg Soffía Árnadóttir,&nbsp;Josse van Dobben de Bruyn,&nbsp;Prem Nigam Kar,&nbsp;David E. Roberson,&nbsp;Peter Zeman","doi":"10.1112/jlms.70141","DOIUrl":"https://doi.org/10.1112/jlms.70141","url":null,"abstract":"<p>Sabidussi's theorem [Duke Math. J. <b>28</b> (1961), 573–578] gives necessary and sufficient conditions under which the automorphism group of a lexicographic product of two graphs is a wreath product of the respective automorphism groups. We prove a quantum version of Sabidussi's theorem for finite graphs, with the automorphism groups replaced by quantum automorphism groups and the wreath product replaced by the free wreath product of quantum groups. This extends the result of Chassaniol [J. Algebra <b>456</b>, 2016, 23–45], who proved it for regular graphs. Moreover, we apply our result to lexicographic products of quantum vertex transitive graphs, determining their quantum automorphism groups even when Sabidussi's conditions do not apply.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70141","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793552","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":"Elliptic-to-parabolic Morrey spaces–potentials–capacities with applications to certain evolution PDE","authors":"David R. Adams,&nbsp;Jie Xiao","doi":"10.1112/jlms.70131","DOIUrl":"https://doi.org/10.1112/jlms.70131","url":null,"abstract":"<p>This article shows the optimal parabolic generalizations of some known strong–weak results for the elliptic Morrey spaces–potentials–capacities, thereby studying not only the heat-type equations but also the Navier–Stokes-type equations as well as the wave-type equations living within the elliptic-to-parabolic Morrey spaces.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793553","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":"Some applications of canonical metrics to Landau–Ginzburg models","authors":"Jacopo Stoppa","doi":"10.1112/jlms.70148","DOIUrl":"https://doi.org/10.1112/jlms.70148","url":null,"abstract":"<p>It is known that a given smooth del Pezzo surface or Fano threefold <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> admits a choice of log Calabi–Yau compactified mirror toric Landau–Ginzburg model (with respect to certain fixed Kähler classes and Gorenstein toric degenerations). Here we consider the problem of constructing a corresponding map <span></span><math>\u0000 <semantics>\u0000 <mi>Θ</mi>\u0000 <annotation>$Theta$</annotation>\u0000 </semantics></math> from a domain in the complexified Kähler cone of <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> to a well-defined, separated moduli space <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$mathfrak {M}$</annotation>\u0000 </semantics></math> of polarised manifolds endowed with a canonical metric. We prove a complete result for del Pezzos and a partial result for some special Fano threefolds. The construction uses some fundamental results in the theory of constant scalar curvature Kähler metrics. As a consequence <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$mathfrak {M}$</annotation>\u0000 </semantics></math> parametrises <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-stable manifolds and the domain of <span></span><math>\u0000 <semantics>\u0000 <mi>Θ</mi>\u0000 <annotation>$Theta$</annotation>\u0000 </semantics></math> is endowed with the pullback of a Weil–Petersson form.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70148","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143778240","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":"Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations","authors":"Giuseppe Ancona,&nbsp;Mattia Cavicchi,&nbsp;Robert Laterveer,&nbsp;Giulia Saccà","doi":"10.1112/jlms.70133","DOIUrl":"https://doi.org/10.1112/jlms.70133","url":null,"abstract":"<p>We show that the hyper-Kähler varieties of OG10-type constructed by Laza–Saccà–Voisin (LSV) verify the Lefschetz standard conjecture. This is an application of a more general result, stating that certain Lagrangian fibrations verify this conjecture. The main technical assumption of this general result is that the Lagrangian fibration satisfies the hypotheses of Ngô's support theorem. Verifying that the LSV tenfolds do satisfy those hypotheses is of independent interest. Another point of independent interest of the paper is the definition and the study of the Lefschetz standard conjecture in the relative setting, and its relation to the classical absolute case.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70133","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143770173","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":"Regular homotopy classes of links of simple singularities and immersions associated with their Dynkin diagrams","authors":"Masato Tanabe","doi":"10.1112/jlms.70140","DOIUrl":"https://doi.org/10.1112/jlms.70140","url":null,"abstract":"<p>Our aim is to determine the regular homotopy classes of immersions related to Arnol'd's simple singularities. For every type of simple singularities, we determine the regular homotopy class of the inclusion map of the link into the 5-sphere. We further show that the inclusion map is regularly homotopic to the immersion associated with the corresponding Dynkin diagram, which was constructed by Kinjo. We prove these by computing the complete invariants of the immersions given by Wu and Saeki–Szűcs–Takase. As an application, we also determine the Smale invariants of Kinjo's immersions.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143770174","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":"Nondensity results in high-dimensional stable Hamiltonian topology","authors":"Robert Cardona,&nbsp;Fabio Gironella","doi":"10.1112/jlms.70143","DOIUrl":"https://doi.org/10.1112/jlms.70143","url":null,"abstract":"<p>We push forward the study of higher dimensional stable Hamiltonian topology by establishing two nondensity results. First, we prove that stable hypersurfaces are not <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$C^3$</annotation>\u0000 </semantics></math>-dense in any isotopy class of embedded hypersurfaces on any ambient symplectic manifold of dimension <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>8</mn>\u0000 </mrow>\u0000 <annotation>$2ngeqslant 8$</annotation>\u0000 </semantics></math>. Our second result is that on any manifold of dimension <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>m</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 <mo>⩾</mo>\u0000 <mn>5</mn>\u0000 </mrow>\u0000 <annotation>$2m+1geqslant 5$</annotation>\u0000 </semantics></math>, the set of non-degenerate stable Hamiltonian structures is not <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$C^2$</annotation>\u0000 </semantics></math>-dense among stable Hamiltonian structures in any given stable homotopy class that satisfies a mild assumption. The latter generalizes a result by Cieliebak and Volkov to arbitrary dimensions.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143770172","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}