{
  "id": "1406.2444",
  "version": "v2",
  "published": "2014-06-10T07:21:21.000Z",
  "updated": "2015-04-20T13:29:39.000Z",
  "title": "Umbilicity and characterization of Pansu spheres in the Heisenberg group",
  "authors": [
    "Jih-Hsin Cheng",
    "Hung-Lin Chiu",
    "Jenn-Fang Hwang",
    "Paul Yang"
  ],
  "comment": "32 pages, 2 figures; in Crelle's journal, 2015",
  "categories": [
    "math.DG"
  ],
  "abstract": "For $n\\geq 2$ we define a notion of umbilicity for hypersurfaces in the Heisenberg group $H_{n}$. We classify umbilic hypersurfaces in some cases, and prove that Pansu spheres are the only umbilic spheres with positive constant $p$(or horizontal)-mean curvature in $H_{n}$ up to Heisenberg translations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-10T07:21:21.000Z",
      "comment": "31 pages, 2 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-20T13:29:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "32V20",
      "35L80",
      "35J70",
      "49Q10"
    ],
    "keywords": [
      "pansu spheres",
      "heisenberg group",
      "umbilicity",
      "characterization",
      "heisenberg translations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.2444C"
    }
  }
}