超曲面的对称性与Hopf引理

IF 1.4 4区工程技术 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Mathematics in Engineering Pub Date : 2022-05-10 DOI:10.3934/mine.2023084

Yanyan Li

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引用次数: 1

摘要

A.D.Alexandrov的一个经典定理说，欧氏空间中具有常平均曲率的连通紧致光滑超曲面必须是球面。我们给出了关于具有有序平均曲率的超曲面的对称性的一些结果以及Hopf引理的相关变化。将讨论一些悬而未决的问题。

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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Symmetry of hypersurfaces and the Hopf Lemma

A classical theorem of A. D. Alexandrov says that a connected compact smooth hypersurface in Euclidean space with constant mean curvature must be a sphere. We give exposition to some results on symmetry properties of hypersurfaces with ordered mean curvature and associated variations of the Hopf Lemma. Some open problems will be discussed.

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