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arXiv · 1708.06861

Uniqueness of stable capillary hypersurfaces in a ball

Guofang Wang·Chao Xia
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Abstract

In this paper we prove that any immersed stable capillary hypersurfaces in a ball in space forms are totally umbilical. This solves completely a long-standing open problem. In the proof one of crucial ingredients is a new Minkowski type formula. We also prove a Heintze-Karcher-Ros type inequality for hypersurfaces in a ball, which, together with the new Minkowski formula, yields a new proof of Alexandrov's Theorem for embedded CMC hypersurfaces in a ball with free boundary.

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Guofang Wang, Chao Xia. 2017-08-23. Uniqueness of stable capillary hypersurfaces in a ball. https://doi.org/10.1007/s00208-019-01845-0

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