{
  "id": "1708.06861",
  "version": "v1",
  "published": "2017-08-23T00:48:08.000Z",
  "updated": "2017-08-23T00:48:08.000Z",
  "title": "Uniqueness of stable capillary hypersurfaces in a ball",
  "authors": [
    "Guofang Wang",
    "Chao Xia"
  ],
  "comment": "30 pages, 1 figure",
  "categories": [
    "math.DG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-23T00:48:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniqueness",
      "heintze-karcher-ros type inequality",
      "minkowski type formula",
      "immersed stable capillary hypersurfaces",
      "embedded cmc hypersurfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}