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

Differential Geometry 2024-05-09 v1

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.

Keywords

Cite

@article{arxiv.2211.02913,
  title  = {Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space},
  author = {Xiaohan Jia and Guofang Wang and Chao Xia and Xuwen Zhang},
  journal= {arXiv preprint arXiv:2211.02913},
  year   = {2024}
}

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16 pages