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Boundary rigidity of Gromov hyperbolic spaces 格罗莫夫双曲空间的边界刚性
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-09-06 DOI: 10.1007/s10711-024-00947-7
Hao Liang, Qingshan Zhou
{"title":"Boundary rigidity of Gromov hyperbolic spaces","authors":"Hao Liang, Qingshan Zhou","doi":"10.1007/s10711-024-00947-7","DOIUrl":"https://doi.org/10.1007/s10711-024-00947-7","url":null,"abstract":"<p>We introduce the concept of boundary rigidity for Gromov hyperbolic spaces. We show that a proper geodesic Gromov hyperbolic space with a pole is boundary rigid if and only if its Gromov boundary is uniformly perfect. As an application, we show that for a non-compact Gromov hyperbolic complete Riemannian manifold or a Gromov hyperbolic uniform graph, boundary rigidity is equivalent to having positive Cheeger isoperimetric constant and also to being nonamenable. Moreover, several hyperbolic fillings of compact metric spaces are proved to be boundary rigid if and only if the metric spaces are uniformly perfect. Also, boundary rigidity is shown to be equivalent to being geodesically rich, a concept introduced by Shchur (J Funct Anal 264(3):815–836, 2013).</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"25 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142193949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Meanders, hyperelliptic pillowcase covers, and the Johnson filtration 蜿蜒曲折、超椭圆枕套和约翰逊滤波器
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-08-08 DOI: 10.1007/s10711-024-00936-w
Luke Jeffreys
{"title":"Meanders, hyperelliptic pillowcase covers, and the Johnson filtration","authors":"Luke Jeffreys","doi":"10.1007/s10711-024-00936-w","DOIUrl":"https://doi.org/10.1007/s10711-024-00936-w","url":null,"abstract":"<p>We provide minimal constructions of meanders with particular combinatorics. Using these meanders, we give minimal constructions of hyperelliptic pillowcase covers with a single horizontal cylinder and simultaneously a single vertical cylinder so that one or both of the core curves are separating curves on the underlying surface. In the case where both of the core curves are separating, we use these surfaces in a construction of Aougab–Taylor in order to prove that for any hyperelliptic connected component of the moduli space of quadratic differentials with no poles there exist ratio-optimising pseudo-Anosovs lying arbitrarily deep in the Johnson filtration and stabilising the Teichmüller disk of a quadratic differential lying in this connected component.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"93 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Topology of horocycles on geometrically finite nonpositively curved surfaces 几何有限非正曲面上的角环拓扑学
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-07-28 DOI: 10.1007/s10711-024-00941-z
Sergi Burniol Clotet
{"title":"Topology of horocycles on geometrically finite nonpositively curved surfaces","authors":"Sergi Burniol Clotet","doi":"10.1007/s10711-024-00941-z","DOIUrl":"https://doi.org/10.1007/s10711-024-00941-z","url":null,"abstract":"<p>We study the closure of horocycles on rank 1 nonpositively curved surfaces with finitely generated fundamental group. Each horocycle is closed or dense on a certain subset of the unit tangent bundle. In fact, we classify each half-horocycle in terms of the associated geodesic rays. We also determine the nonwandering set of the horocyclic flow and characterize the surfaces admitting a minimal set for this flow.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"45 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Domains of discontinuity of Lorentzian affine group actions 洛伦兹仿射群作用的不连续域
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-07-24 DOI: 10.1007/s10711-024-00940-0
Michael Kapovich, Bernhard Leeb
{"title":"Domains of discontinuity of Lorentzian affine group actions","authors":"Michael Kapovich, Bernhard Leeb","doi":"10.1007/s10711-024-00940-0","DOIUrl":"https://doi.org/10.1007/s10711-024-00940-0","url":null,"abstract":"<p>We prove nonemptyness of domains of proper discontinuity of Anosov groups of affine Lorentzian transformations of <span>({mathbb R}^n)</span>.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"11 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The octanomial normal forms of cubic surfaces with applications to automorphisms 立方曲面的八叉法线形式及其在自动形态中的应用
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-07-20 DOI: 10.1007/s10711-024-00931-1
China Kaneko
{"title":"The octanomial normal forms of cubic surfaces with applications to automorphisms","authors":"China Kaneko","doi":"10.1007/s10711-024-00931-1","DOIUrl":"https://doi.org/10.1007/s10711-024-00931-1","url":null,"abstract":"<p>We will show that in any characteristic every nonsingular cubic surface is projectively isomorphic to the surface given by the octanomial normal form. This normal form is discovered in Panizzut et al. (LeMatematiche 75(2), 2020) only in characteristic 0 by exhaustive computer search. We offer a conceptual explanation that has the added benefit of being characteristic free. As an application, we give octanomial normal forms of the strata of the coarse moduli space of cubic surfaces defined in Dolgachev and Duncan (Compos Math 25(1):1–59, 1972) which preserve most specialization with respect to automorphisms.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"43 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141742571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The density of Meissner polyhedra 迈斯纳多面体的密度
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-07-19 DOI: 10.1007/s10711-024-00933-z
Ryan Hynd
{"title":"The density of Meissner polyhedra","authors":"Ryan Hynd","doi":"10.1007/s10711-024-00933-z","DOIUrl":"https://doi.org/10.1007/s10711-024-00933-z","url":null,"abstract":"<p>We consider Meissner polyhedra in <span>(mathbb {R}^3)</span>. These are constant width bodies whose boundaries consist of pieces of spheres and spindle tori. We define these shapes by taking appropriate intersections of congruent balls and show that they are dense within the space of constant width bodies in the Hausdorff topology. This density assertion was essentially established by Sallee. However, we offer a modern viewpoint taking into consideration the recent progress in understanding ball polyhedra and in constructing constant width bodies based on these shapes.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"7 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141742572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lower bound for KVol on the minimal stratum of translation surfaces 平移面最小层上 KVol 的下限
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-07-10 DOI: 10.1007/s10711-024-00937-9
Julien Boulanger
{"title":"Lower bound for KVol on the minimal stratum of translation surfaces","authors":"Julien Boulanger","doi":"10.1007/s10711-024-00937-9","DOIUrl":"https://doi.org/10.1007/s10711-024-00937-9","url":null,"abstract":"<p>In this paper we are interested in algebraic intersection of closed curves of a given length on translation surfaces. We study the quantity KVol, defined in Cheboui et al. (Bull Soc Math France 149(4):613–640, 2021) and studied in Cheboui et al. (2021), Cheboui et al. (C R Math Acad Sci Paris 359:65–70, 2021), Boulanger et al. (Ann Henri Lebesgue, 2024), and Boulanger (Algebraic intersection, lengths and Veech surfaces, 2023. arXiv:2309.17165), and we construct families of translation surfaces in each connected component of the minimal stratum <span>(mathcal {H}(2g-2))</span> of the moduli space of translation surfaces of genus <span>(g ge 2)</span> such that KVol is arbitrarily close to the genus of the surface, which is conjectured to be the infimum of KVol on <span>(mathcal {H}(2g-2))</span>.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141584574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A criterion for Lie algebroid connections on a compact Riemann surface 紧凑黎曼面上的 Lie algebroid 连接标准
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-07-01 DOI: 10.1007/s10711-024-00938-8
Indranil Biswas, Pradip Kumar, Anoop Singh
{"title":"A criterion for Lie algebroid connections on a compact Riemann surface","authors":"Indranil Biswas, Pradip Kumar, Anoop Singh","doi":"10.1007/s10711-024-00938-8","DOIUrl":"https://doi.org/10.1007/s10711-024-00938-8","url":null,"abstract":"<p>Let <i>X</i> be a compact connected Riemann surface and <span>((V,, phi ))</span> a holomorphic Lie algebroid on <i>X</i> such that the holomorphic vector bundle <i>V</i> is stable. We give a necessary and sufficient condition on holomorphic vector bundles <i>E</i> on <i>X</i> to admit a Lie algebroid connection.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"36 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Trisecting a 4-dimensional book into three chapters 将四维图书分成三章
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-06-25 DOI: 10.1007/s10711-024-00932-0
Marc Kegel, Felix Schmäschke
{"title":"Trisecting a 4-dimensional book into three chapters","authors":"Marc Kegel, Felix Schmäschke","doi":"10.1007/s10711-024-00932-0","DOIUrl":"https://doi.org/10.1007/s10711-024-00932-0","url":null,"abstract":"<p>We describe an algorithm that takes as input an open book decomposition of a closed oriented 4-manifold and outputs an explicit trisection diagram of that 4-manifold. Moreover, a slight variation of this algorithm also works for open books on manifolds with non-empty boundary and for 3-manifold bundles over <span>(S^1)</span>. We apply this algorithm to several simple open books, demonstrate that it is compatible with various topological constructions, and argue that it generalizes and unifies several previously known constructions.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"93 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Projectively induced Kähler cones over regular Sasakian manifolds 规则萨萨基流形上的投影诱导凯勒锥
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-06-24 DOI: 10.1007/s10711-024-00935-x
Stefano Marini, Nicoletta Tardini, Michela Zedda
{"title":"Projectively induced Kähler cones over regular Sasakian manifolds","authors":"Stefano Marini, Nicoletta Tardini, Michela Zedda","doi":"10.1007/s10711-024-00935-x","DOIUrl":"https://doi.org/10.1007/s10711-024-00935-x","url":null,"abstract":"<p>Motivated by a conjecture in Loi et al. (Math Zeit 290:599–613, 2018) we prove that the Kähler cone over a regular complete Sasakian manifold is Ricci-flat and projectively induced if and only if it is flat. We also obtain that, up to <span>(mathcal D_a)</span>—homothetic transformations, Kähler cones over homogeneous compact Sasakian manifolds are projectively induced. As main tool we provide a relation between the Kähler potentials of the transverse Kähler metric and of the cone metric.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"10 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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