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Geometriae Dedicata最新文献

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Topological aspects of the space of metric measure spaces 度量空间的拓扑方面
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-04-11 DOI: 10.1007/s10711-024-00921-3
Daisuke Kazukawa, Hiroki Nakajima, Takashi Shioya
{"title":"Topological aspects of the space of metric measure spaces","authors":"Daisuke Kazukawa, Hiroki Nakajima, Takashi Shioya","doi":"10.1007/s10711-024-00921-3","DOIUrl":"https://doi.org/10.1007/s10711-024-00921-3","url":null,"abstract":"<p>Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces and developed the convergence theory of metric measure spaces. We investigate several topological properties on the space equipped with these distance functions toward a deep understanding of convergence theory.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577951","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
Branching laws of Klein four-symmetric pairs for $$textrm{Sp}(n,mathbb {R})$$ $$textrm{Sp}(n,mathbb {R})$$ 的克莱因四对称对的分支规律
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-04-11 DOI: 10.1007/s10711-024-00922-2
Jiaying Ding, Haian He, Huangyuan Pan, Lifu Wang
{"title":"Branching laws of Klein four-symmetric pairs for $$textrm{Sp}(n,mathbb {R})$$","authors":"Jiaying Ding, Haian He, Huangyuan Pan, Lifu Wang","doi":"10.1007/s10711-024-00922-2","DOIUrl":"https://doi.org/10.1007/s10711-024-00922-2","url":null,"abstract":"<p>For the real symplectic groups <span>(G=textrm{Sp}(n,mathbb {R}))</span>, we classify all the Klein four-symmetric pairs <span>((G,G^Gamma ))</span>, and determine whether there exist infinite-dimensional irreducible <span>((mathfrak {g},K))</span>-modules discretely decomposable upon restriction to <span>(G^Gamma )</span>. As a consequence, we obtain a similar result to Chen and He (Int J Math 34(1):2250094, 2023, Corollary 21).</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577828","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 Nielsen realization problem for high degree del Pezzo surfaces 高阶德尔佩佐曲面的尼尔森实现问题
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-04-08 DOI: 10.1007/s10711-024-00912-4
Seraphina Eun Bi Lee
{"title":"The Nielsen realization problem for high degree del Pezzo surfaces","authors":"Seraphina Eun Bi Lee","doi":"10.1007/s10711-024-00912-4","DOIUrl":"https://doi.org/10.1007/s10711-024-00912-4","url":null,"abstract":"<p>Let <i>M</i> be a smooth 4-manifold underlying some del Pezzo surface of degree <span>(d ge 6)</span>. We consider the smooth Nielsen realization problem for <i>M</i>: which finite subgroups of <span>({{,textrm{Mod},}}(M) = pi _0({{,textrm{Homeo},}}^+(M)))</span> have lifts to <span>({{,textrm{Diff},}}^+(M) le {{,textrm{Homeo},}}^+(M))</span> under the quotient map <span>(pi : {{,textrm{Homeo},}}^+(M) rightarrow {{,textrm{Mod},}}(M))</span>? We give a complete classification of such finite subgroups of <span>({{,textrm{Mod},}}(M))</span> for <span>(d ge 7)</span> and a partial answer for <span>(d = 6)</span>. For the cases <span>(d ge 8)</span>, the quotient map <span>(pi )</span> admits a section with image contained in <span>({{,textrm{Diff},}}^+(M))</span>. For the case <span>(d = 7)</span>, we show that all finite order elements of <span>({{,textrm{Mod},}}(M))</span> have lifts to <span>({{,textrm{Diff},}}^+(M))</span>, but there are finite subgroups of <span>({{,textrm{Mod},}}(M))</span> that do not lift to <span>({{,textrm{Diff},}}^+(M))</span>. We prove that the condition of whether a finite subgroup <span>(G le {{,textrm{Mod},}}(M))</span> lifts to <span>({{,textrm{Diff},}}^+(M))</span> is equivalent to the existence of a certain equivariant connected sum realizing <i>G</i>. For the case <span>(d = 6)</span>, we show this equivalence for all maximal finite subgroups <span>(G le {{,textrm{Mod},}}(M))</span>.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577830","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
On the Teichmüller stack of compact quotients of $${text {SL}}_2({mathbb {C}})$$ 论 $${text {SL}}_2({mathbb {C}})$$ 的紧凑商的泰希米勒堆栈
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-04-04 DOI: 10.1007/s10711-024-00916-0
Théo Jamin
{"title":"On the Teichmüller stack of compact quotients of $${text {SL}}_2({mathbb {C}})$$","authors":"Théo Jamin","doi":"10.1007/s10711-024-00916-0","DOIUrl":"https://doi.org/10.1007/s10711-024-00916-0","url":null,"abstract":"<p>This article aims to pursue and generalize, by using the global point of view offered by the stacks, the local study made by <span>Ghys</span> (J für die reine und angewandte Mathematik 468:113–138, 1995) concerning the deformations of complex structures of compact quotients of <span>({text {SL}}_2({mathbb {C}}))</span>. In his article, <span>Ghys</span> showed that the analytic germ of the representation variety <span>({mathcal {R}}(varGamma ):={text {Hom}}(varGamma ,{text {SL}}_2({mathbb {C}})))</span> of <span>(varGamma )</span> in <span>({text {SL}}_2({mathbb {C}}))</span>, pointed at the trivial morphism, determines the Kuranishi space of <span>({text {SL}}_2({mathbb {C}})/varGamma )</span>. In this note, we show that the tautological family above a Zariski analytic open subset <i>V</i> in <span>({mathcal {R}}(varGamma ))</span> remains complete. Moreover, the computation of the isotropy group of a complex structure in Teichmüller space, allows us to affirm that the quotient stack <span>([V/{text {SL}}_2({mathbb {C}})])</span> is an open substack of the Teichmüller stack of <span>({text {SL}}_2({mathbb {C}})/varGamma )</span>.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577949","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
Boundary metric of Epstein-Penner convex hull and discrete conformality 爱泼斯坦-彭纳凸壳的边界度量和离散保角性
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-04-03 DOI: 10.1007/s10711-024-00901-7
Xin Nie
{"title":"Boundary metric of Epstein-Penner convex hull and discrete conformality","authors":"Xin Nie","doi":"10.1007/s10711-024-00901-7","DOIUrl":"https://doi.org/10.1007/s10711-024-00901-7","url":null,"abstract":"<p>The Epstein-Penner convex hull construction associates to every decorated punctured hyperbolic surface a convex set in the Minkowski space. It works in the de Sitter and anti-de Sitter spaces as well. In these three spaces, the quotient of the spacelike boundary part of the convex set has an induced Euclidean, spherical and hyperbolic metric, respectively, with conical singularities. We show that this gives a bijection from the decorated Teichmüller space to a moduli space of such metrics in the Euclidean and hyperbolic cases, as well as a bijection between specific subspaces of them in the spherical case. Moreover, varying the decoration of a fixed hyperbolic surface corresponds to a discrete conformal change of the metric. This gives a new 3-dimensional interpretation of discrete conformality which is in a sense inverse to the Bobenko-Pinkall-Springborn interpretation.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577732","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
Variation of holonomy for projective structures and an application to drilling hyperbolic 3-manifolds 投影结构的整体性变化及其在钻孔双曲3-manifolds中的应用
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-04-03 DOI: 10.1007/s10711-024-00908-0
Martin Bridgeman, Kenneth Bromberg
{"title":"Variation of holonomy for projective structures and an application to drilling hyperbolic 3-manifolds","authors":"Martin Bridgeman, Kenneth Bromberg","doi":"10.1007/s10711-024-00908-0","DOIUrl":"https://doi.org/10.1007/s10711-024-00908-0","url":null,"abstract":"<p>We bound the derivative of complex length of a geodesic under variation of the projective structure on a closed surface in terms of the norm of the Schwarzian in a neighborhood of the geodesic. One application is to cone-manifold deformations of acylindrical hyperbolic 3-manifolds.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577738","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
Halfspaces and hypersurfaces in the bidisk 双盘中的半空间和超曲面
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-04-03 DOI: 10.1007/s10711-024-00917-z
Virginie Charette, Youngju Kim
{"title":"Halfspaces and hypersurfaces in the bidisk","authors":"Virginie Charette, Youngju Kim","doi":"10.1007/s10711-024-00917-z","DOIUrl":"https://doi.org/10.1007/s10711-024-00917-z","url":null,"abstract":"<p>We construct a halfspace in the bidisk, whose boundary acts like a bisector. As an application, we build a fundamental domain consisting of such halfspaces for the action of groups that project to Schottky groups in both factors.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577740","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
Correction: Intersection theory and volumes of moduli spaces of flat metrics on the sphere 更正：球面上平面度量的交点理论和模量空间的体积
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-04-03 DOI: 10.1007/s10711-024-00909-z
{"title":"Correction: Intersection theory and volumes of moduli spaces of flat metrics on the sphere","authors":"","doi":"10.1007/s10711-024-00909-z","DOIUrl":"https://doi.org/10.1007/s10711-024-00909-z","url":null,"abstract":"","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140747761","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
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":null,"pages":null},"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":null,"pages":null},"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
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