Uniqueness of stable capillary hypersurfaces in a ball

Guofang Wang Albert-Ludwigs University of Freiburg Chao Xia Xiamen University

Differential Geometry mathscidoc:2106.10001

Mathematische Annalen, 374, (3), 1845-1882, 2019.8
In this paper we prove that any immersed stable capillary hypersurfaces in a ball in space forms are totally umbilical. %either a totally geodesic disk or a spherical cap. Our result also provides a proof of a conjecture proposed by Sternberg-Zumbrun in {\it J Reine Angew Math 503 (1998), 63--85}. We also prove a Heintze-Karcher-Ros type inequality for hypersurfaces with free boundary 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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  title={Uniqueness of stable capillary hypersurfaces in a ball},
  author={Guofang Wang, and Chao Xia},
  booktitle={Mathematische Annalen},
Guofang Wang, and Chao Xia. Uniqueness of stable capillary hypersurfaces in a ball. 2019. Vol. 374. In Mathematische Annalen. pp.1845-1882. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210616145503703935840.
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