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Geometriae Dedicata最新文献

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Minimal surfaces and Colding-Minicozzi entropy in complex hyperbolic space 复双曲空间中的极小曲面和科尔丁-米尼科齐熵
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-04-03 DOI: 10.1007/s10711-024-00906-2
Jacob Bernstein, Arunima Bhattacharya
{"title":"Minimal surfaces and Colding-Minicozzi entropy in complex hyperbolic space","authors":"Jacob Bernstein, Arunima Bhattacharya","doi":"10.1007/s10711-024-00906-2","DOIUrl":"https://doi.org/10.1007/s10711-024-00906-2","url":null,"abstract":"<p>We study notions of asymptotic regularity for a class of minimal submanifolds of complex hyperbolic space that includes minimal Lagrangian submanifolds. As an application, we show a relationship between an appropriate formulation of Colding-Minicozzi entropy and a quantity we call the <i>CR</i>-volume that is computed from the asymptotic geometry of such submanifolds.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"43 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577950","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
Continuous deformation of the Bowen-Series map associated to a cocompact triangle group 与协整三角形群相关的鲍温系列图的连续变形
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-04-02 DOI: 10.1007/s10711-024-00887-2
{"title":"Continuous deformation of the Bowen-Series map associated to a cocompact triangle group","authors":"","doi":"10.1007/s10711-024-00887-2","DOIUrl":"https://doi.org/10.1007/s10711-024-00887-2","url":null,"abstract":"<h3>Abstract</h3> <p>In 1979, for each signature for Fuchsian groups of the first kind, Bowen and Series constructed an explicit fundamental domain for one group of the signature, and from this a function on <span> <span>({mathbb {S}}^1)</span> </span> tightly associated with this group. In general, their fundamental domain enjoys what has since been called both the ‘extension property’ and the ‘even corners property’. We determine the exact set of signatures for cocompact triangle groups for which this property can hold for any convex fundamental domain, and verify that for this restricted set, the Bowen-Series fundamental domain does have the property. To each Bowen-Series function in this corrected setting, we naturally associate four continuous deformation families of circle functions. We show that each of these functions is aperiodic if and only if it is surjective; and, is finite Markov if and only if its natural parameter is a hyperbolic fixed point of the triangle group at hand.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"32 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578025","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
Prym representations of the handlebody group 手柄体群的普赖姆表征
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-03-29 DOI: 10.1007/s10711-024-00911-5
{"title":"Prym representations of the handlebody group","authors":"","doi":"10.1007/s10711-024-00911-5","DOIUrl":"https://doi.org/10.1007/s10711-024-00911-5","url":null,"abstract":"<h3>Abstract</h3> <p>Let <em>S</em> be an oriented, closed surface of genus <em>g</em>. The mapping class group of <em>S</em> is the group of orientation preserving homeomorphisms of <em>S</em> modulo isotopy. In 1997, Looijenga introduced the Prym representations, which are virtual representations of the mapping class group that depend on a finite, abelian group. Let <em>V</em> be a genus <em>g</em> handlebody with boundary <em>S</em>. The handlebody group is the subgroup of those mapping classes of <em>S</em> that extend over <em>V</em>. The twist group is the subgroup of the handlebody group generated by twists about meridians. Here, we restrict the Prym representations to the handlebody group and further to the twist group. We determine the image of the representations in the cyclic case.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"47 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577943","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
Mirror stabilizers for lattice complex hyperbolic triangle groups 晶格复双曲三角群的镜像稳定器
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-03-26 DOI: 10.1007/s10711-024-00910-6
Martin Deraux
{"title":"Mirror stabilizers for lattice complex hyperbolic triangle groups","authors":"Martin Deraux","doi":"10.1007/s10711-024-00910-6","DOIUrl":"https://doi.org/10.1007/s10711-024-00910-6","url":null,"abstract":"<p>For each lattice complex hyperbolic triangle group, we study the Fuchsian stabilizers of (reprentatives of each group orbit of) mirrors of complex reflections. We give explicit generators for the stabilizers, and compute their signature in the sense of Fuchsian groups. For some groups, we also find explicit pairs of complex lines such that the union of their stabilizers generate the ambient lattice.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"21 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315858","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
K3 surfaces with two involutions and low Picard number 具有两个渐开线和低皮卡数的 K3 曲面
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-03-13 DOI: 10.1007/s10711-024-00900-8
Dino Festi, Wim Nijgh, Daniel Platt
{"title":"K3 surfaces with two involutions and low Picard number","authors":"Dino Festi, Wim Nijgh, Daniel Platt","doi":"10.1007/s10711-024-00900-8","DOIUrl":"https://doi.org/10.1007/s10711-024-00900-8","url":null,"abstract":"<p>Let <i>X</i> be a complex algebraic K3 surface of degree 2<i>d</i> and with Picard number <span>(rho )</span>. Assume that <i>X</i> admits two commuting involutions: one holomorphic and one anti-holomorphic. In that case, <span>(rho ge 1)</span> when <span>(d=1)</span> and <span>(rho ge 2)</span> when <span>(d ge 2)</span>. For <span>(d=1)</span>, the first example defined over <span>({mathbb {Q}})</span> with <span>(rho =1)</span> was produced already in 2008 by Elsenhans and Jahnel. A K3 surface provided by Kondō, also defined over <span>({mathbb {Q}})</span>, can be used to realise the minimum <span>(rho =2)</span> for all <span>(dge 2)</span>. In these notes we construct new explicit examples of K3 surfaces over the rational numbers realising the minimum <span>(rho =2)</span> for <span>(d=2,3,4)</span>. We also show that a nodal quartic surface can be used to realise the minimum <span>(rho =2)</span> for infinitely many different values of <i>d</i>. Finally, we strengthen a result of Morrison by showing that for any even lattice <i>N</i> of rank <span>(1le r le 10)</span> and signature <span>((1,r-1))</span> there exists a K3 surface <i>Y</i> defined over <span>({mathbb {R}})</span> such that <span>({{,textrm{Pic},}}Y_{mathbb {C}}={{,textrm{Pic},}}Y cong N)</span>.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"26 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125414","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
Left-invariant distributions diffeomorphic to flat distributions 左变分布与平面分布的衍射关系
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-03-13 DOI: 10.1007/s10711-024-00905-3
Sebastiano Nicolussi Golo, Alessandro Ottazzi
{"title":"Left-invariant distributions diffeomorphic to flat distributions","authors":"Sebastiano Nicolussi Golo, Alessandro Ottazzi","doi":"10.1007/s10711-024-00905-3","DOIUrl":"https://doi.org/10.1007/s10711-024-00905-3","url":null,"abstract":"<p>For a stratified group <i>G</i>, we construct a class of Lie groups endowed with a left-invariant distribution locally diffeomorphic to the flat distribution of <i>G</i>. Vice versa, we show that all Lie groups with a left-invariant distribution that is locally diffeomorphic to the flat distribution of <i>G</i> belong to the class we constructed, if the Lie algebra of <i>G</i> has finite Tanaka prolongation.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"10 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125261","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 geometric characterization of cyclic p-gonal surfaces 循环 p 角曲面的几何特征
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-03-13 DOI: 10.1007/s10711-024-00902-6
Daniel M. Gallo
{"title":"A geometric characterization of cyclic p-gonal surfaces","authors":"Daniel M. Gallo","doi":"10.1007/s10711-024-00902-6","DOIUrl":"https://doi.org/10.1007/s10711-024-00902-6","url":null,"abstract":"<p>A closed Riemann surface <i>S</i> of genus <span>(gge 2)</span> is called <i>cyclic p-gonal</i> if it has an automorphism <span>(rho )</span> of order <i>p</i>, where <i>p</i> is a prime, such that <span>(S/langle rho rangle )</span> has genus 0. For <span>(p=2)</span>, the surface is called hyperelliptic and <span>(rho )</span> is an involution with <span>(2g+2)</span> fixed points. Classicaly, cyclic p-gonal surfaces can be characterized using Fuchsian groups. In this paper we establish a geometric characterization of cyclic p-gonal surfaces. Specifically, this is determined by collections of simple geodesic arcs on the surfaces and graphs associated to these arcs. In previous work, the author has given a geometric characterization of hyperelliptic surfaces in terms of simple, closed geodesics and graphs associated to these. The present work may be seen as an extension. Involutions, however, have properties that do not generalize to arbitrary automorphisms of order <i>p</i>. Hence, the number of vertices needed in the graphs used here is larger than that of the hyperelliptic case.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"68 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125647","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
Rupert property of some particular n-simplices and n-octahedrons 一些特定 n 正简和 n 正八面体的鲁珀特性质
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-03-06 DOI: 10.1007/s10711-024-00894-3
Pongbunthit Tonpho, Wacharin Wichiramala
{"title":"Rupert property of some particular n-simplices and n-octahedrons","authors":"Pongbunthit Tonpho, Wacharin Wichiramala","doi":"10.1007/s10711-024-00894-3","DOIUrl":"https://doi.org/10.1007/s10711-024-00894-3","url":null,"abstract":"<p>Three hundred years ago, Prince Rupert of Rhine showed that a unit cube has the property that one copy of it can be passed through a suitable hole in another copy. Under this situation, we say that a unit cube has the Rupert property. In the past years, there are many research studying about the Rupert property of many solids in <span>(mathbb {R}^3)</span>. For higher dimensions, the <i>n</i>-dimensional cube and the regular <i>n</i>-simplex were studied to have the Rupert property. In this work, we focus on the Rupert property of some polyhedrons in <i>n</i> dimensions. In particular, we show that some particular <i>n</i>-dimensional simplices, generalized <i>n</i>-dimensional octahedrons and some related solids in <span>(mathbb {R}^n)</span> have the Rupert property using arbitrarily small rotations and translations.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"33 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140045022","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
Curvature bounds on length-minimizing discs 长度最小化圆盘的曲率边界
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-03-06 DOI: 10.1007/s10711-024-00892-5
{"title":"Curvature bounds on length-minimizing discs","authors":"","doi":"10.1007/s10711-024-00892-5","DOIUrl":"https://doi.org/10.1007/s10711-024-00892-5","url":null,"abstract":"<p>We show that a length-minimizing disk inherits the upper curvature bound of the target. As a consequence we prove that harmonic discs and ruled discs inherit the upper curvature bound from the ambient space.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"76 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140045332","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
Cusped Borel Anosov representations with positivity 具有正向性的有簇玻雷阿诺索夫表征
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-03-06 DOI: 10.1007/s10711-024-00895-2
Gye-Seon Lee, Tengren Zhang
{"title":"Cusped Borel Anosov representations with positivity","authors":"Gye-Seon Lee, Tengren Zhang","doi":"10.1007/s10711-024-00895-2","DOIUrl":"https://doi.org/10.1007/s10711-024-00895-2","url":null,"abstract":"<p>We show that if a cusped Borel Anosov representation from a lattice <span>(Gamma subset textsf{PGL}_2({{,mathrm{mathbb {R}},}}))</span> to <span>(textsf{PGL}_d({{,mathrm{mathbb {R}},}}))</span> contains a unipotent element with a single Jordan block in its image, then it is necessarily a (cusped) Hitchin representation. We also show that the amalgamation of a Hitchin representation with a cusped Borel Anosov representation that is not Hitchin is never cusped Borel Anosov.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"41 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140044804","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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