{
  "id": "1410.2404",
  "version": "v1",
  "published": "2014-10-09T09:46:23.000Z",
  "updated": "2014-10-09T09:46:23.000Z",
  "title": "A remark on compact hypersurfaces with constant mean curvature in space forms",
  "authors": [
    "Giovanni Catino"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this note we characterize compact hypersurfaces of dimension $n\\geq 2$ with constant mean curvature $H$ immersed in space forms of constant curvature and satisfying an optimal integral pinching condition: they are either totally umbilical or, when $n\\geq 3$ and $H\\neq 0$, they are contained in a rotational hypersurface. In dimension two, the integral pinching condition reduces to a topological assumption and we recover the classical Hopf-Chern result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-09T09:46:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constant mean curvature",
      "space forms",
      "optimal integral pinching condition",
      "integral pinching condition reduces",
      "rotational hypersurface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.2404C"
    }
  }
}