Uniqueness of stable capillary hypersurfaces in a ball
Differential Geometry
2019-05-23 v2
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.
Keywords
Cite
@article{arxiv.1708.06861,
title = {Uniqueness of stable capillary hypersurfaces in a ball},
author = {Guofang Wang and Chao Xia},
journal= {arXiv preprint arXiv:1708.06861},
year = {2019}
}
Comments
Final version, Math. Ann., to appear