{
  "id": "0704.1021",
  "version": "v2",
  "published": "2007-04-09T16:46:05.000Z",
  "updated": "2008-01-25T14:28:20.000Z",
  "title": "Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds",
  "authors": [
    "Claus Gerhardt"
  ],
  "comment": "9 pages, v2:final version, to be published",
  "journal": "Adv. Calc. Var. 1, 123--132 (2008)",
  "doi": "10.1515/ACV.2008.004",
  "categories": [
    "math.DG"
  ],
  "abstract": "We prove curvature estimates for general curvature functions. As an application we show the existence of closed, strictly convex hypersurfaces with prescribed curvature $F$, where the defining cone of $F$ is $\\C_+$. $F$ is only assumed to be monotone, symmetric, homogeneous of degree 1, concave and of class $C^{m,\\al}$, $m\\ge4$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-01-25T14:28:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "53C21",
      "53C44",
      "53C50",
      "58J05"
    ],
    "keywords": [
      "curvature estimates",
      "weingarten hypersurfaces",
      "riemannian manifolds",
      "general curvature functions",
      "strictly convex hypersurfaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.1021G"
    }
  }
}