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Iterated monodromy group of a PCF quadratic non-polynomial map PCF 二次非多项式映射的迭代单色群
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-04-02 DOI: 10.1007/s00229-024-01549-z
Özlem Ejder, Yasemin Kara, Ekin Ozman
{"title":"Iterated monodromy group of a PCF quadratic non-polynomial map","authors":"Özlem Ejder, Yasemin Kara, Ekin Ozman","doi":"10.1007/s00229-024-01549-z","DOIUrl":"https://doi.org/10.1007/s00229-024-01549-z","url":null,"abstract":"<p>We study the postcritically finite non-polynomial map <span>(f(x)=frac{1}{(x-1)^2})</span> over a number field <i>k</i> and prove various results about the geometric <span>(G^{textrm{geom}}(f))</span> and arithmetic <span>(G^{textrm{arith}}(f))</span> iterated monodromy groups of <i>f</i>. We show that the elements of <span>(G^{textrm{geom}}(f))</span> are the ones in <span>(G^{textrm{arith}}(f))</span> that fix certain roots of unity by assuming a conjecture on the size of <span>(G^{textrm{geom}}_n(f))</span>. Furthermore, we describe exactly for which <span>(a in k)</span> the Arboreal Galois group <span>(G_a(f))</span> and <span>(G^{textrm{arith}}(f))</span> are equal.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"130 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598132","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
Some functional inequalities under lower Bakry–Émery–Ricci curvature bounds with $${varepsilon }$$ -range 具有 $${{varepsilon }$$ 范围的 Bakry-Émery-Ricci 曲率下限下的一些函数不等式
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-04-02 DOI: 10.1007/s00229-024-01537-3
Yasuaki Fujitani
{"title":"Some functional inequalities under lower Bakry–Émery–Ricci curvature bounds with $${varepsilon }$$ -range","authors":"Yasuaki Fujitani","doi":"10.1007/s00229-024-01537-3","DOIUrl":"https://doi.org/10.1007/s00229-024-01537-3","url":null,"abstract":"<p>For <i>n</i>-dimensional weighted Riemannian manifolds, lower <i>m</i>-Bakry–Émery–Ricci curvature bounds with <span>({varepsilon })</span>-range, introduced by Lu-Minguzzi-Ohta (Anal Geom Metr Spaces 10(1):1–30, 2022), integrate constant lower bounds and certain variable lower bounds in terms of weight functions. In this paper, we prove a Cheng type inequality and a local Sobolev inequality under lower <i>m</i>-Bakry–Émery–Ricci curvature bounds with <span>({varepsilon })</span>-range. These generalize those inequalities under constant curvature bounds for <span>(m in (n,infty ))</span> to <span>(min (-infty ,1]cup {infty })</span>.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"26 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598138","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
Submanifolds with constant Moebius curvature and flat normal bundle 具有恒定莫比乌斯曲率和平坦法线束的子曲率
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-04-01 DOI: 10.1007/s00229-024-01536-4
M. S. R. Antas, R. Tojeiro
{"title":"Submanifolds with constant Moebius curvature and flat normal bundle","authors":"M. S. R. Antas, R. Tojeiro","doi":"10.1007/s00229-024-01536-4","DOIUrl":"https://doi.org/10.1007/s00229-024-01536-4","url":null,"abstract":"<p>We classify isometric immersions <span>(f:M^{n}rightarrow mathbb {R}^{n+p})</span>, <span>(n ge 5)</span> and <span>(2p le n)</span>, with constant Moebius curvature and flat normal bundle.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"130 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598131","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
Local Galois representations associated to additive polynomials 与加法多项式相关的局部伽罗瓦表示
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-30 DOI: 10.1007/s00229-024-01550-6
Takahiro Tsushima
{"title":"Local Galois representations associated to additive polynomials","authors":"Takahiro Tsushima","doi":"10.1007/s00229-024-01550-6","DOIUrl":"https://doi.org/10.1007/s00229-024-01550-6","url":null,"abstract":"<p>For an additive polynomial and a positive integer, we define an irreducible smooth representation of a Weil group of a non-archimedean local field. We study several invariants of this representation. We obtain a necessary and sufficient condition for it to be primitive.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"52 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598135","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
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
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
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