Curvature exponent and geodesic dimension on Sard-regular Carnot groups

IF 0.9 3区数学 Q2 MATHEMATICS Analysis and Geometry in Metric Spaces Pub Date : 2024-07-26 DOI:10.1515/agms-2024-0004

Sebastiano Nicolussi Golo, Ye Zhang

{"title":"Curvature exponent and geodesic dimension on Sard-regular Carnot groups","authors":"Sebastiano Nicolussi Golo, Ye Zhang","doi":"10.1515/agms-2024-0004","DOIUrl":null,"url":null,"abstract":"In this study, we characterize the geodesic dimension <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>N</m:mi> </m:mrow> <m:mrow> <m:mi mathvariant=\"normal\">GEO</m:mi> </m:mrow> </m:msub> </m:math> {N}_{{\\rm{GEO}}} and give a new lower bound to the curvature exponent <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>N</m:mi> </m:mrow> <m:mrow> <m:mi mathvariant=\"normal\">CE</m:mi> </m:mrow> </m:msub> </m:math> {N}_{{\\rm{CE}}} on Sard-regular Carnot groups. As an application, we give an example of step-two Carnot group on which <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>N</m:mi> </m:mrow> <m:mrow> <m:mi mathvariant=\"normal\">CE</m:mi> </m:mrow> </m:msub> <m:mo>></m:mo> <m:msub> <m:mrow> <m:mi>N</m:mi> </m:mrow> <m:mrow> <m:mi mathvariant=\"normal\">GEO</m:mi> </m:mrow> </m:msub> </m:math> {N}_{{\\rm{CE}}}\\gt {N}_{{\\rm{GEO}}} ; this answers a question posed by Rizzi (Measure contraction properties of Carnot groups. Calc. Var. Partial Differential Equations 55 (2016), no. 3, Art. 60, 20).","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Geometry in Metric Spaces","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/agms-2024-0004","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

In this study, we characterize the geodesic dimension

N GEO

{N}_{{\rm{GEO}}}

and give a new lower bound to the curvature exponent

N CE

{N}_{{\rm{CE}}}

on Sard-regular Carnot groups. As an application, we give an example of step-two Carnot group on which

N CE > N GEO

{N}_{{\rm{CE}}}\gt {N}_{{\rm{GEO}}}

; this answers a question posed by Rizzi (Measure contraction properties of Carnot groups. Calc. Var. Partial Differential Equations 55 (2016), no. 3, Art. 60, 20).

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

萨德规则卡诺群上的曲率指数和测地维度

在本研究中，我们描述了测地维 N GEO {N}_{\rm{GEO}} 的特征，并给出了沙特规则卡诺群上曲率指数 N CE {N}_{\rm{CE}} 的新下限。作为应用，我们给出了一个阶二卡诺群的例子，其中 N CE > N GEO {N}_{{\rm{CE}}}\gt {N}_{{\rm{GEO}}} ；这回答了里齐提出的一个问题（卡诺群的度量收缩性质.Calc.Calc.Partial Differential Equations 55 (2016), no.3, Art.60, 20).

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.

期刊最新文献

Qualitative Lipschitz to bi-Lipschitz decomposition On a critical Choquard-Kirchhoff p-sub-Laplacian equation in ℍ n Curvature exponent and geodesic dimension on Sard-regular Carnot groups On the heat kernel of the Rumin complex and Calderón reproducing formula Metric quasiconformality and Sobolev regularity in non-Ahlfors regular spaces