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arXiv · 2211.02913

Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space

Xiaohan Jia·Guofang Wang·Chao Xia·Xuwen Zhang
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Abstract

In this paper, we show that any embedded capillary hypersurface in the half-space with anisotropic constant mean curvature is a truncated Wulff shape. This extends Wente's result \cite{Wente80} to the anisotropic case and He-Li-Ma-Ge's result \cite{HLMG09} to the capillary boundary case. The main ingredients in the proof are a new Heintze-Karcher inequality and a new Minkowski formula, which have their own inetrest.

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Xiaohan Jia, Guofang Wang, Chao Xia, Xuwen Zhang. 2022-11-05. Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space. https://doi.org/10.1007/s00205-023-01861-0

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