{
  "id": "1212.2052",
  "version": "v4",
  "published": "2012-12-10T13:17:47.000Z",
  "updated": "2013-02-18T15:30:00.000Z",
  "title": "Ricci curvature and $L^p$-convergence",
  "authors": [
    "Shouhei Honda"
  ],
  "comment": "65 pages. Theorem 1.6 and Corollary 4.19 added",
  "categories": [
    "math.DG",
    "math.FA",
    "math.MG"
  ],
  "abstract": "We give the definition of $L^p$-convergence of tensor fields with respect to the Gromov-Hausdorff topology and several fundamental properties of the convergence. We apply this to establish a Bochner-type inequality which keeps the term of Hessian on the Gromov-Hausdorff limit space of a sequence of Riemannian manifolds with a lower Ricci curvature bound and to give a geometric explicit formula for the Dirichlet Laplacian on a limit space defined by Cheeger-Colding. We also prove a continuity of the first eigenvalues of the p-Laplacian with respect to the Gromov-Hausdorff topology.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-02-18T15:30:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convergence",
      "lower ricci curvature bound",
      "gromov-hausdorff topology",
      "gromov-hausdorff limit space",
      "geometric explicit formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 65,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.2052H"
    }
  }
}