海森堡集团的CMC球体

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2016-11-24 DOI:10.1515/agms-2019-0006

Valentina Franceschi, F. Montefalcone, R. Monti

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引用次数: 6

摘要

摘要研究了黎曼海森堡群H1中的一类常平均曲率球族。这些球体被推测为H1的等周集合。我们证明了几个支持这个猜想的结果。我们也将注意力集中在次黎曼极限上。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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CMC Spheres in the Heisenberg Group

Abstract We study a family of spheres with constant mean curvature (CMC) in the Riemannian Heisenberg group H1. These spheres are conjectured to be the isoperimetric sets of H1. We prove several results supporting this conjecture. We also focus our attention on the sub-Riemannian limit.

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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.