Convex Hull Property and Exclosure Theorems for H-Minimal Hypersurfaces in Carnot Groups

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2016-09-20 DOI:10.1515/agms-2016-0008

F. Montefalcone

引用次数: 0

Abstract

Abstract In this paper, we generalize to sub-Riemannian Carnot groups some classical results in the theory of minimal submanifolds. Our main results are for step 2 Carnot groups. In this case, we will prove the convex hull property and some “exclosure theorems” for H-minimal hypersurfaces of class C2 satisfying a Hörmander-type condition.

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卡诺群中h -极小超曲面的凸包性质及包合定理

摘要本文将最小子流形理论中的一些经典结果推广到次黎曼卡诺群。我们的主要结果是针对第二步卡诺群的。在这种情况下，我们将证明满足Hörmander-type条件的C2类h -极小超曲面的凸包性质和一些“闭包定理”。

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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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.