Advances in Mathematics最新文献

{"title":"Helly-type theorems, CAT(0) spaces, and actions of automorphism groups of free groups","authors":"Martin R. Bridson","doi":"10.1016/j.aim.2025.110343","DOIUrl":"10.1016/j.aim.2025.110343","url":null,"abstract":"<div><div>We prove a variety of fixed-point theorems for groups acting on CAT(0) spaces. Fixed points are obtained by a bootstrapping technique, whereby increasingly large subgroups are proved to have fixed points: specific configurations in the subgroup lattice of Γ are exhibited and Helly-type theorems are developed to prove that the fixed-point sets of the subgroups in the configuration intersect. In this way, we obtain lower bounds on the smallest dimension <span><math><mrow><mi>FixDim</mi></mrow><mo>(</mo><mi>Γ</mi><mo>)</mo><mo>+</mo><mn>1</mn></math></span> in which various groups of geometric interest can act on a complete CAT(0) space without a global fixed point. For automorphism groups of free groups, we prove <span><math><mrow><mi>FixDim</mi></mrow><mo>(</mo><mrow><mi>Aut</mi></mrow><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>)</mo><mo>≥</mo><mo>⌊</mo><mn>2</mn><mi>n</mi><mo>/</mo><mn>3</mn><mo>⌋</mo></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"475 ","pages":"Article 110343"},"PeriodicalIF":1.5,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068794","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":"Local well-posedness of the incompressible current-vortex sheet problems","authors":"Sicheng Liu ,&nbsp;Zhouping Xin","doi":"10.1016/j.aim.2025.110339","DOIUrl":"10.1016/j.aim.2025.110339","url":null,"abstract":"<div><div>We prove the local well-posedness of the incompressible current-vortex sheet problems in standard Sobolev spaces under the surface tension or the Syrovatskij condition, which shows that both capillary forces and large tangential magnetic fields can stabilize the motion of current-vortex sheets. Furthermore, under the Syrovatskij condition, the vanishing surface tension limit is established for the motion of current-vortex sheets. These results hold without assuming the interface separating the two plasmas being a graph.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"475 ","pages":"Article 110339"},"PeriodicalIF":1.5,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068796","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":"Shifted coisotropic structures for differentiable stacks","authors":"Maxence Mayrand","doi":"10.1016/j.aim.2025.110345","DOIUrl":"10.1016/j.aim.2025.110345","url":null,"abstract":"<div><div>We introduce a notion of coisotropics on 1-shifted symplectic Lie groupoids (i.e. quasi-symplectic groupoids) using twisted Dirac structures and show that it satisfies properties analogous to the corresponding derived-algebraic notion in shifted Poisson geometry. In particular, intersections of 1-coisotropics are 0-shifted Poisson. We also show that 1-shifted coisotropic structures transfer through Morita equivalences, giving a well-defined notion for differentiable stacks. Most results are formulated with clean-intersection conditions weaker than transversality while avoiding derived geometry. Examples of 1-coisotropics that are not necessarily Lagrangians include Hamiltonian actions of quasi-symplectic groupoids on Dirac manifolds, and this recovers several generalizations of Marsden–Weinstein–Meyer's symplectic reduction via intersection and Morita transfer.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"475 ","pages":"Article 110345"},"PeriodicalIF":1.5,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068798","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":"Frobenius monoidal functors from ambiadjunctions and their lifts to Drinfeld centers","authors":"Johannes Flake ,&nbsp;Robert Laugwitz ,&nbsp;Sebastian Posur","doi":"10.1016/j.aim.2025.110344","DOIUrl":"10.1016/j.aim.2025.110344","url":null,"abstract":"<div><div>We identify general conditions, formulated using the projection formula morphisms, for a functor that is simultaneously left and right adjoint to a strong monoidal functor to be a Frobenius monoidal functor. Moreover, we identify stronger conditions for the adjoint functor to extend to a braided Frobenius monoidal functor on Drinfeld centers building on our previous work in <span><span>[14]</span></span>. As an application, we construct concrete examples of (braided) Frobenius monoidal functors obtained from morphisms of Hopf algebras via induction.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"475 ","pages":"Article 110344"},"PeriodicalIF":1.5,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068797","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":"Binary forms with the same value set III. The case of D3 and D6","authors":"Étienne Fouvry ,&nbsp;Peter Koymans","doi":"10.1016/j.aim.2025.110326","DOIUrl":"10.1016/j.aim.2025.110326","url":null,"abstract":"<div><div>Let <span><math><mi>F</mi><mo>,</mo><mi>G</mi><mo>∈</mo><mi>Z</mi><mo>[</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>]</mo></math></span> be binary forms of degree ≥3 with automorphism groups isomorphic to the dihedral group of cardinality 6 or 12. We characterize exactly when <em>F</em> and <em>G</em> have the same value set, i.e. <span><math><mi>F</mi><mo>(</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>=</mo><mi>G</mi><mo>(</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"475 ","pages":"Article 110326"},"PeriodicalIF":1.5,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948136","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":"New bounds for Stein's square functions in higher dimensions","authors":"Shengwen Gan ,&nbsp;Changkeun Oh ,&nbsp;Shukun Wu","doi":"10.1016/j.aim.2025.110342","DOIUrl":"10.1016/j.aim.2025.110342","url":null,"abstract":"<div><div>We improve the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> bounds on Stein's square function to the best-known range of the Fourier restriction problem when <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span>. Applications, including certain local smoothing estimates, are also discussed.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"475 ","pages":"Article 110342"},"PeriodicalIF":1.5,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942831","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":"Curvature homogeneous hypersurfaces in space forms","authors":"Robert Bryant ,&nbsp;Luis Florit ,&nbsp;Wolfgang Ziller","doi":"10.1016/j.aim.2025.110338","DOIUrl":"10.1016/j.aim.2025.110338","url":null,"abstract":"<div><div>We provide a classification of curvature homogeneous hypersurfaces in space forms by classifying the ones in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>. In higher dimensions, besides the isoparametric and the constant curvature ones, there is a single one in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>5</mn></mrow></msup></math></span>. Besides the obvious examples, we show that there exists an isolated hypersurface with a circle of symmetries and a one parameter family admitting no continuous symmetries. Outside the set of minimal points, which only exists in the case of <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>, every example is, locally and up to covers, of this form.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"475 ","pages":"Article 110338"},"PeriodicalIF":1.5,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942832","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":"Convex elements and Steinberg's cross-sections","authors":"Sian Nie ,&nbsp;Panjun Tan ,&nbsp;Qingchao Yu","doi":"10.1016/j.aim.2025.110346","DOIUrl":"10.1016/j.aim.2025.110346","url":null,"abstract":"<div><div>In this paper, we study convex elements in a (twisted) Weyl group introduced by Ivanov and the first named author. We show that each conjugacy class of the twisted Weyl group contains a convex element, and moreover, the Steinberg cross-sections exist for all convex elements. This result strictly enlarges the cases of Steinberg cross-sections from a new perspective, and will play an essential role in the study of higher Deligne-Lusztig representations.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"475 ","pages":"Article 110346"},"PeriodicalIF":1.5,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942830","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":"Grothendieck-Verdier module categories, Frobenius algebras and relative Serre functors","authors":"Jürgen Fuchs ,&nbsp;Gregor Schaumann ,&nbsp;Christoph Schweigert ,&nbsp;Simon Wood","doi":"10.1016/j.aim.2025.110325","DOIUrl":"10.1016/j.aim.2025.110325","url":null,"abstract":"<div><div>We develop the theory of module categories over a Grothendieck-Verdier category <span><math><mi>C</mi></math></span>, i.e. a monoidal category with a dualizing object and hence a duality structure more general than rigidity. Such a category comes with two monoidal structures ⊗ and <figure><img></figure> which are related by non-invertible morphisms and which we treat on an equal footing. Quite generally, non-invertible structure morphisms play a dominant role in this theory. In any Grothendieck-Verdier module category <span><math><mi>M</mi></math></span> we find two distinguished subcategories <figure><img></figure> and <span><math><msup><mrow><mover><mrow><mi>M</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mo>⊗</mo></mrow></msup></math></span>, which can be characterized by certain structure morphisms being actually invertible. The internal Hom <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>m</mi></mrow></msub><mspace></mspace><mo>:</mo><mo>=</mo><munder><mrow><mrow><mi>Hom</mi></mrow></mrow><mo>_</mo></munder><mo>(</mo><mi>m</mi><mo>,</mo><mi>m</mi><mo>)</mo></math></span> of an object <em>m</em> in <span><math><msup><mrow><mover><mrow><mi>M</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mo>⊗</mo></mrow></msup></math></span> that is a <span><math><mi>C</mi></math></span>-generator is an algebra such that <span><math><mrow><mi>mod</mi></mrow><mtext>-</mtext><msub><mrow><mi>A</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> is equivalent to <span><math><mi>M</mi></math></span> as a module category. Crucially, the subcategories <figure><img></figure> and <span><math><msup><mrow><mover><mrow><mi>M</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mo>⊗</mo></mrow></msup></math></span> are precisely those on which a relative Serre functor can be defined. This relative Serre functor furnishes an equivalence <figure><img></figure>, and any isomorphism <span><math><mi>m</mi><mspace></mspace><mover><mrow><mo>→</mo></mrow><mrow><mspace></mspace><mo>≅</mo><mspace></mspace></mrow></mover><mspace></mspace><mi>S</mi><mo>(</mo><mi>m</mi><mo>)</mo></math></span> endows the algebra <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> with the structure of a Grothendieck-Verdier Frobenius algebra.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"475 ","pages":"Article 110325"},"PeriodicalIF":1.5,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942829","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 Ricci iteration towards cscK metrics","authors":"Kewei Zhang","doi":"10.1016/j.aim.2025.110340","DOIUrl":"10.1016/j.aim.2025.110340","url":null,"abstract":"<div><div>Motivated by the problem of finding constant scalar curvature Kähler metrics, we investigate a Ricci iteration sequence of Rubinstein that discretizes the pseudo-Calabi flow. While the long time existence of the flow is still an open question, we show that the iteration sequence does exist for all steps, along which the K-energy decreases. We further show that the iteration sequence, modulo automorphisms, converges smoothly to a constant scalar curvature Kähler metric if there is one, thus confirming a conjecture of Rubinstein from 2007 and extending results of Darvas–Rubinstein to arbitrary Kähler classes.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"475 ","pages":"Article 110340"},"PeriodicalIF":1.5,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942833","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}