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Mathematische Annalen最新文献

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Median geometry for spaces with measured walls and for groups. 中间几何与测量的墙壁和群体的空间。
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2025-10-25 DOI: 10.1007/s00208-025-03289-1
Indira Chatterji, Cornelia Druţu
{"title":"Median geometry for spaces with measured walls and for groups.","authors":"Indira Chatterji, Cornelia Druţu","doi":"10.1007/s00208-025-03289-1","DOIUrl":"https://doi.org/10.1007/s00208-025-03289-1","url":null,"abstract":"<p><p>We show that uniform lattices of isometries of products of real hyperbolic spaces act properly discontinuously and cocompactly on a median space. For lattices in products of at least two factors, this is the strongest degree of compatibility possible with median geometry. The result follows from an analysis of a quasification of median geometry that provides a geometric characterization of spaces at a finite Hausdorff distance from a median space. The case of complex hyperbolic metric spaces is different; we show that these spaces cannot be at finite Hausdorff distance from a median space.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"393 3-4","pages":"2925-2952"},"PeriodicalIF":1.4,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12827449/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146052861","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}
引用次数: 0
A Toponogov globalisation result for Lorentzian length spaces. 洛伦兹长度空间的Toponogov全球化结果。
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2025-05-07 DOI: 10.1007/s00208-025-03167-w
Tobias Beran, John Harvey, Lewis Napper, Felix Rott
{"title":"A Toponogov globalisation result for Lorentzian length spaces.","authors":"Tobias Beran, John Harvey, Lewis Napper, Felix Rott","doi":"10.1007/s00208-025-03167-w","DOIUrl":"10.1007/s00208-025-03167-w","url":null,"abstract":"<p><p>In the synthetic geometric setting introduced by Kunzinger and Sämann, we present an analogue of Toponogov's Globalisation Theorem which applies to Lorentzian length spaces with lower (timelike) curvature bounds. Our approach utilises a \"cat's cradle\" construction akin to that which appears in several proofs in the metric setting. On the road to our main result, we also provide a lemma regarding the subdivision of triangles in spaces with a local lower curvature bound and a synthetic Lorentzian version of the Lebesgue Number Lemma. Several properties of time functions and the null distance on globally hyperbolic Lorentzian length spaces are also highlighted. We conclude by presenting several applications of our results, including versions of the Bonnet-Myers Theorem and the Splitting Theorem for Lorentzian length spaces with local lower curvature bounds, as well as discussion of stability of curvature bounds under Gromov-Hausdorff convergence.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 3","pages":"3447-3478"},"PeriodicalIF":1.4,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12310883/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144775718","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}
引用次数: 0
The wavefront set: bounds for the Langlands parameter. 朗兰兹参数的波前集边界。
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2025-09-09 DOI: 10.1007/s00208-025-03278-4
Dan Ciubotaru, Ju-Lee Kim
{"title":"The wavefront set: bounds for the Langlands parameter.","authors":"Dan Ciubotaru, Ju-Lee Kim","doi":"10.1007/s00208-025-03278-4","DOIUrl":"https://doi.org/10.1007/s00208-025-03278-4","url":null,"abstract":"<p><p>For an irreducible smooth representation of a connected reductive <i>p</i>-adic group, two important associated invariants are the wavefront set and the (partly conjectural) Langlands parameter. While a wavefront set consists of <i>p</i>-adic nilpotent orbits, one constituent of the Langlands parameter is a complex nilpotent orbit in the dual Lie algebra. For unipotent representations in the sense of Lusztig, the corresponding nilpotent orbits on the two sides are related via the Lusztig-Spaltenstein duality (Ciubotaru et al. in Am J Math arXiv:2112.14354v4, J Reine Angew Math (Crelles J) 823:191-253, 2025). In this paper, we formulate a general upper-bound conjecture and several variants relating the nilpotent orbits that appear in the wavefront set and in the Langlands parameter. We also verify these expectations in some cases, including the depth-zero supercuspidal representations of classical groups and all the irreducible representations of <math><msub><mi>G</mi> <mn>2</mn></msub> </math> .</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"393 2","pages":"1827-1861"},"PeriodicalIF":1.4,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12559080/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145401168","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}
引用次数: 0
Evolution problems with perturbed 1-Laplacian type operators on random walk spaces. 随机游走空间上扰动1-拉普拉斯算子的演化问题。
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2025-05-21 DOI: 10.1007/s00208-025-03180-z
W Górny, J M Mazón, J Toledo
{"title":"Evolution problems with perturbed 1-Laplacian type operators on random walk spaces.","authors":"W Górny, J M Mazón, J Toledo","doi":"10.1007/s00208-025-03180-z","DOIUrl":"https://doi.org/10.1007/s00208-025-03180-z","url":null,"abstract":"<p><p>Random walk spaces are a general framework for the study of PDEs. They include as particular cases locally finite weighted connected graphs and nonlocal settings involving symmetric integrable kernels on <math> <msup><mrow><mi>R</mi></mrow> <mi>N</mi></msup> </math> . We are interested in the study of evolution problems involving two random walk structures so that the associated functionals have different growth on each structure. We also deal with the case of a functional with different growth on a partition of the random walk.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 3","pages":"3895-3957"},"PeriodicalIF":1.4,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12310885/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144775719","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}
引用次数: 0
Regular logarithmic connections. 正则对数连接。
IF 1.3 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2024-12-03 DOI: 10.1007/s00208-024-03047-9
Piotr Achinger
{"title":"Regular logarithmic connections.","authors":"Piotr Achinger","doi":"10.1007/s00208-024-03047-9","DOIUrl":"https://doi.org/10.1007/s00208-024-03047-9","url":null,"abstract":"<p><p>We introduce the notion of a regular integrable connection on a smooth log scheme over <math><mi>C</mi></math> and construct an equivalence between the category of such connections and the category of integrable connections on its analytification, compatible with de Rham cohomology. This extends the work of Deligne (when the log structure is trivial), and combined with the work of Ogus yields a topological description of the category of regular connections in terms of certain constructible sheaves on the Kato-Nakayama space. The key ingredients are the notion of a canonical extension in this context and the existence of good compactifications of log schemes obtained recently by Włodarczyk.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"391 4","pages":"5293-5339"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11954731/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143753555","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}
引用次数: 0
A unified Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups. 由多个阿贝尔群标记的图中圈的统一Erdős-Pósa定理。
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2025-09-26 DOI: 10.1007/s00208-025-03293-5
J Pascal Gollin, Kevin Hendrey, O-Joung Kwon, Sang-Il Oum, Youngho Yoo
{"title":"A unified Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups.","authors":"J Pascal Gollin, Kevin Hendrey, O-Joung Kwon, Sang-Il Oum, Youngho Yoo","doi":"10.1007/s00208-025-03293-5","DOIUrl":"https://doi.org/10.1007/s00208-025-03293-5","url":null,"abstract":"<p><p>In 1965, Erdős and Pósa proved that there is an (approximate) duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold for odd cycles, and Dejter and Neumann-Lara asked in 1988 to find all pairs  <math><mrow><mo>(</mo> <mi>ℓ</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo></mrow> </math> of integers where such a duality holds for the family of cycles of length  <math><mi>ℓ</mi></math> modulo <i>z</i>. We characterise all such pairs, and we further generalise this characterisation to cycles in graphs labelled with a bounded number of abelian groups, whose values avoid a bounded number of elements of each group. This unifies almost all known types of cycles that admit such a duality, and it also provides new results. Moreover, we characterise the obstructions to such a duality in this setting, and thereby obtain an analogous characterisation for cycles in graphs embeddable on a fixed compact orientable surface.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"393 2","pages":"2507-2559"},"PeriodicalIF":1.4,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12559191/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145401170","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}
引用次数: 0
Transversality of holomorphic maps into hyperquadrics. 全纯映射到超二次曲面的横向性。
IF 1.3 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2025-03-26 DOI: 10.1007/s00208-025-03134-5
Xiaojun Huang, Weixia Zhu
{"title":"Transversality of holomorphic maps into hyperquadrics.","authors":"Xiaojun Huang, Weixia Zhu","doi":"10.1007/s00208-025-03134-5","DOIUrl":"https://doi.org/10.1007/s00208-025-03134-5","url":null,"abstract":"<p><p>We study holomorphic maps <i>F</i> from a smooth Levi non-degenerate real hypersurface <math> <mrow><msub><mi>M</mi> <mi>ℓ</mi></msub> <mo>⊂</mo> <msup><mrow><mi>C</mi></mrow> <mi>n</mi></msup> </mrow> </math> into a hyperquadric <math><msubsup><mi>H</mi> <mrow><msup><mi>ℓ</mi> <mo>'</mo></msup> </mrow> <mi>N</mi></msubsup> </math> with signatures <math><mrow><mi>ℓ</mi> <mo>≤</mo> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> <mo>/</mo> <mn>2</mn></mrow> </math> and <math> <mrow><msup><mi>ℓ</mi> <mo>'</mo></msup> <mo>≤</mo> <mrow><mo>(</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo></mrow> <mo>/</mo> <mn>2</mn> <mo>,</mo></mrow> </math> respectively. Assuming that <math><mrow><mi>N</mi> <mo>-</mo> <mi>n</mi> <mo><</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo></mrow> </math> we prove that if <math><mrow><mi>ℓ</mi> <mo>=</mo> <msup><mi>ℓ</mi> <mo>'</mo></msup> <mo>,</mo></mrow> </math> then <i>F</i> is either CR transversal to <math><msubsup><mi>H</mi> <mrow><mi>ℓ</mi></mrow> <mi>N</mi></msubsup> </math> at every point of <math> <mrow><msub><mi>M</mi> <mi>ℓ</mi></msub> <mo>,</mo></mrow> </math> or it maps a neighborhood of <math><msub><mi>M</mi> <mi>ℓ</mi></msub> </math> in <math> <msup><mrow><mi>C</mi></mrow> <mi>n</mi></msup> </math> into <math> <mrow><msubsup><mi>H</mi> <mrow><mi>ℓ</mi></mrow> <mi>N</mi></msubsup> <mo>.</mo></mrow> </math> Furthermore, in the case where <math> <mrow><msup><mi>ℓ</mi> <mo>'</mo></msup> <mo>></mo> <mi>ℓ</mi> <mo>,</mo></mrow> </math> we show that if <i>F</i> is not CR transversal at <math><mrow><mn>0</mn> <mo>∈</mo> <msub><mi>M</mi> <mi>ℓ</mi></msub> <mo>,</mo></mrow> </math> then it must be transversally flat. The latter is best possible.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 2","pages":"1731-1746"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12084281/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144094324","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}
引用次数: 0
Quasisymmetries of finitely ramified Julia sets. 有限分支Julia集的拟对称。
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2025-09-02 DOI: 10.1007/s00208-025-03238-y
James Belk, Bradley Forrest
{"title":"Quasisymmetries of finitely ramified Julia sets.","authors":"James Belk, Bradley Forrest","doi":"10.1007/s00208-025-03238-y","DOIUrl":"https://doi.org/10.1007/s00208-025-03238-y","url":null,"abstract":"<p><p>We develop a theory of quasisymmetries for finitely ramified fractals, with applications to finitely ramified Julia sets. We prove that certain finitely ramified fractals admit a naturally defined class of \"undistorted metrics\" that are all quasisymmetrically equivalent. As a result, piecewise-defined homeomorphisms of such a fractal that locally preserve the cell structure are quasisymmetries. This immediately gives a solution to the quasisymmetric uniformization problem for topologically rigid fractals such as the Sierpiński triangle. We show that our theory applies to many finitely ramified Julia sets, and we prove that any connected Julia set for a hyperbolic unicritical polynomial has infinitely many quasisymmetries, generalizing a result of Lyubich and Merenkov. We also prove that the quasisymmetry group of the Julia set for the rational function [Formula: see text] is infinite, and we show that the quasisymmetry groups for the Julia sets of a broad class of polynomials contain Thompson's group <i>F</i>.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"393 2","pages":"1683-1740"},"PeriodicalIF":1.4,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12559074/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145401183","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}
引用次数: 0
Foliation adjunction. 叶片连接
IF 1.3 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2024-12-21 DOI: 10.1007/s00208-024-03067-5
Paolo Cascini, Calum Spicer
{"title":"Foliation adjunction.","authors":"Paolo Cascini, Calum Spicer","doi":"10.1007/s00208-024-03067-5","DOIUrl":"https://doi.org/10.1007/s00208-024-03067-5","url":null,"abstract":"<p><p>We present an adjunction formula for foliations on varieties and we consider applications of the adjunction formula to the cone theorem for rank one foliations and the study of foliation singularities.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"391 4","pages":"5695-5727"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11954749/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143753515","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}
引用次数: 0
Generic solutions of equations involving the modular j function. 包含模j函数的方程的一般解。
IF 1.3 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2025-01-08 DOI: 10.1007/s00208-024-03082-6
Sebastian Eterović
{"title":"Generic solutions of equations involving the modular <i>j</i> function.","authors":"Sebastian Eterović","doi":"10.1007/s00208-024-03082-6","DOIUrl":"https://doi.org/10.1007/s00208-024-03082-6","url":null,"abstract":"<p><p>Assuming a modular version of Schanuel's conjecture and the modular Zilber-Pink conjecture, we show that the existence of generic solutions of certain families of equations involving the modular <i>j</i> function can be reduced to the problem of finding a Zariski dense set of solutions. By imposing some conditions on the field of definition of the variety, we are also able to obtain versions of this result without relying on these conjectures, and even a result including the derivatives of <i>j</i>.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"391 4","pages":"6401-6449"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11954734/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143753525","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}
引用次数: 0
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