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Mathematische Annalen

, Volume 374, Issue 3–4, pp 1845–1882 | Cite as

Uniqueness of stable capillary hypersurfaces in a ball

  • Guofang Wang
  • Chao XiaEmail author
Article

Abstract

In this paper we prove that any immersed stable capillary hypersurfaces in a ball in space forms are totally umbilical. Our result also provides a proof of a conjecture proposed by Sternberg and Zumbrun (J Reine Angew Math 503:63–85, 1998). 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.

Notes

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Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität FreiburgFreiburgGermany
  2. 2.School of Mathematical SciencesXiamen UniversityXiamenPeople’s Republic of China

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