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Desingularization of generic symmetric and generic skew-symmetric determinantal singularities 一般对称和一般偏斜对称行列式奇点的去奇化
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-20 DOI: 10.1007/s00229-024-01544-4
Sabrina Alexandra Gaube, Bernd Schober
{"title":"Desingularization of generic symmetric and generic skew-symmetric determinantal singularities","authors":"Sabrina Alexandra Gaube, Bernd Schober","doi":"10.1007/s00229-024-01544-4","DOIUrl":"https://doi.org/10.1007/s00229-024-01544-4","url":null,"abstract":"<p>We discuss how to resolve generic skew-symmetric and generic symmetric determinantal singularities. The key ingredients are (skew-) symmetry preserving matrix operations in order to deduce an inductive argument.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140203632","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
Weak approximation on Châtelet surfaces 夏特莱曲面上的弱近似
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-18 DOI: 10.1007/s00229-024-01548-0
Masahiro Nakahara, Samuel Roven
{"title":"Weak approximation on Châtelet surfaces","authors":"Masahiro Nakahara, Samuel Roven","doi":"10.1007/s00229-024-01548-0","DOIUrl":"https://doi.org/10.1007/s00229-024-01548-0","url":null,"abstract":"<p>We study weak approximation for Châtelet surfaces over number fields when all singular fibers are defined over rational points. We consider Châtelet surfaces which satisfy weak approximation over every finite extension of the ground field. We prove many of these results by showing that the Brauer–Manin obstruction vanishes, then apply results of Colliot-Thélène, Sansuc, and Swinnerton-Dyer.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"12 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152646","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
Liouville theorem for exponentially harmonic functions on Riemannian manifolds with compact boundary 具有紧凑边界的黎曼流形上指数谐函数的柳维尔定理
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-16 DOI: 10.1007/s00229-024-01543-5
Xinrong Jiang, Jianyi Mao
{"title":"Liouville theorem for exponentially harmonic functions on Riemannian manifolds with compact boundary","authors":"Xinrong Jiang, Jianyi Mao","doi":"10.1007/s00229-024-01543-5","DOIUrl":"https://doi.org/10.1007/s00229-024-01543-5","url":null,"abstract":"<p>In this note, we derive a Yau type gradient estimate for positive exponentially harmonic functions on Riemannian manifolds with compact boundary. As its application, we obtain a Liouville type theorem.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"20 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152738","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
Gromov hyperbolicity and unbounded uniform domains 格罗莫夫双曲性与无界均匀域
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-16 DOI: 10.1007/s00229-024-01546-2
Qingshan Zhou, Yuehui He, Antti Rasila, Tiantian Guan
{"title":"Gromov hyperbolicity and unbounded uniform domains","authors":"Qingshan Zhou, Yuehui He, Antti Rasila, Tiantian Guan","doi":"10.1007/s00229-024-01546-2","DOIUrl":"https://doi.org/10.1007/s00229-024-01546-2","url":null,"abstract":"<p>This paper focuses on Gromov hyperbolic characterizations of unbounded uniform domains. Let <span>(Gsubsetneq mathbb {R}^n)</span> be an unbounded domain. We prove that the following conditions are quantitatively equivalent: (1) <i>G</i> is uniform; (2) <i>G</i> is Gromov hyperbolic with respect to the quasihyperbolic metric and linearly locally connected; (3) <i>G</i> is Gromov hyperbolic with respect to the quasihyperbolic metric and there exists a naturally quasisymmetric correspondence between its Euclidean boundary and the punctured Gromov boundary equipped with a Hamenstädt metric (defined by using a Busemann function). As an application, we investigate the boundary quasisymmetric extensions of quasiconformal mappings, and of more generally rough quasi-isometries between unbounded domains with respect to the quasihyperbolic metrics.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"48 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152913","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
Partial regularity for minimizers of a class of discontinuous Lagrangians 一类不连续拉格朗日最小值的部分正则性
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-14 DOI: 10.1007/s00229-024-01547-1
Roberto Colombo
{"title":"Partial regularity for minimizers of a class of discontinuous Lagrangians","authors":"Roberto Colombo","doi":"10.1007/s00229-024-01547-1","DOIUrl":"https://doi.org/10.1007/s00229-024-01547-1","url":null,"abstract":"<p>We study a one-dimensional Lagrangian problem including the variational reformulation, derived in a recent work of Ambrosio–Baradat–Brenier, of the discrete Monge–Ampère gravitational model, which describes the motion of interacting particles whose dynamics is ruled by the optimal transport problem. The more general action-type functional we consider contains a discontinuous potential term related to the descending slope of the opposite squared distance function from a generic discrete set in <span>(mathbb {R}^{d})</span>. We exploit the underlying geometrical structure provided by the associated Voronoi decomposition of the space to obtain <span>(C^{1,1})</span>-regularity for local minimizers out of a finite number of shock times.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"18 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152648","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
Poisson commutative subalgebras associated with a Cartan subalgebra 与 Cartan 子代数相关的泊松交换子代数
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-13 DOI: 10.1007/s00229-024-01545-3
Oksana S. Yakimova
{"title":"Poisson commutative subalgebras associated with a Cartan subalgebra","authors":"Oksana S. Yakimova","doi":"10.1007/s00229-024-01545-3","DOIUrl":"https://doi.org/10.1007/s00229-024-01545-3","url":null,"abstract":"<p>Let <span>({mathfrak g})</span> be a reductive Lie algebra and <span>(mathfrak tsubset mathfrak g)</span> a Cartan subalgebra. The <span>(mathfrak t)</span>-stable decomposition <span>({mathfrak g}=mathfrak toplus {mathfrak m})</span> yields a bi-grading of the symmetric algebra <span>({mathcal {S}}({mathfrak g}))</span>. The subalgebra <span>({mathcal {Z}}_{({mathfrak g},mathfrak t)})</span> generated by the bi-homogenous components of the symmetric invariants <span>(Fin {mathcal {S}}({mathfrak g})^{mathfrak g})</span> is known to be Poisson commutative. Furthermore the algebra <span>({tilde{{mathcal {Z}}}}=textsf{alg}langle {mathcal {Z}}_{({mathfrak g},{mathfrak t})},{mathfrak t}rangle )</span> is also Poisson commutative. We investigate relations between <span>({tilde{{mathcal {Z}}}})</span> and Mishchenko–Fomenko subalgebras. In type <span>A</span>, we construct a quantisation of <span>({tilde{{mathcal {Z}}}})</span> making use of quantum Mishchenko–Fomenko algebras.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"2013 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152982","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
Hodge numbers of O’Grady 6 via Ngô strings 奥格雷迪的霍奇数 6 通过 Ngô 字符串
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-13 DOI: 10.1007/s00229-024-01540-8
Ben Wu
{"title":"Hodge numbers of O’Grady 6 via Ngô strings","authors":"Ben Wu","doi":"10.1007/s00229-024-01540-8","DOIUrl":"https://doi.org/10.1007/s00229-024-01540-8","url":null,"abstract":"<p>We give an alternative computation of the Betti and Hodge numbers for manifolds of <i>OG</i>6 type using the method of Ngô Strings introduced by de Cataldo, Rapagnetta, and Saccà.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"148 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152735","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
Weights for compact connected Lie groups 紧凑相连李群的权重
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-09 DOI: 10.1007/s00229-024-01538-2
Radha Kessar, Gunter Malle, Jason Semeraro
{"title":"Weights for compact connected Lie groups","authors":"Radha Kessar, Gunter Malle, Jason Semeraro","doi":"10.1007/s00229-024-01538-2","DOIUrl":"https://doi.org/10.1007/s00229-024-01538-2","url":null,"abstract":"<p>Let <span>(ell )</span> be a prime. If <span>(textbf{G})</span> is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from <span>(ell )</span>, and <span>(ell )</span> is a good prime for <span>(textbf{G})</span>, we show that the number of weights of the <span>(ell )</span>-fusion system of <span>(textbf{G})</span> is equal to the number of irreducible characters of its Weyl group. The proof relies on the classification of <span>(ell )</span>-stubborn subgroups in compact Lie groups.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"57 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140105436","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
Upper bounds for the critical values of homology classes of loops 循环同构类临界值的上限
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-02 DOI: 10.1007/s00229-024-01541-7
Hans-Bert Rademacher
{"title":"Upper bounds for the critical values of homology classes of loops","authors":"Hans-Bert Rademacher","doi":"10.1007/s00229-024-01541-7","DOIUrl":"https://doi.org/10.1007/s00229-024-01541-7","url":null,"abstract":"<p>In this short note we discuss upper bounds for the critical values of homology classes in the based and free loop space of compact manifolds carrying a Riemannian or Finsler metric of positive Ricci curvature. In particular it follows that a shortest closed geodesic on a compact and simply-connected <i>n</i>-dimensional manifold of positive Ricci curvature <span>(text {Ric}ge n-1)</span> has length <span>(le n pi .)</span> This improves the bound <span>(8pi (n-1))</span> given by Rotman (Positive Ricci curvature and the length of a shortest periodic geodesic. arXiv:2203.09492, 2022).</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"2 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140018846","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
Diameter estimates for surfaces in conformally flat spaces 共形平面空间中曲面的直径估计值
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-01 DOI: 10.1007/s00229-024-01539-1
Marco Flaim, Christian Scharrer
{"title":"Diameter estimates for surfaces in conformally flat spaces","authors":"Marco Flaim, Christian Scharrer","doi":"10.1007/s00229-024-01539-1","DOIUrl":"https://doi.org/10.1007/s00229-024-01539-1","url":null,"abstract":"<p>The aim of this paper is to give an upper bound for the intrinsic diameter of a surface with boundary immersed in a conformally flat three dimensional Riemannian manifold in terms of the integral of the mean curvature and of the length of its boundary. Of particular interest is the application of the inequality to minimal surfaces in the three-sphere and in the hyperbolic space. Here the result implies an a priori estimate for connected solutions of Plateau’s problem, as well as a necessary condition on the boundary data for the existence of such solutions. The proof follows a construction of Miura and uses a diameter bound for closed surfaces obtained by Topping and Wu–Zheng.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"18 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140018869","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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