{
  "id": "0908.0869",
  "version": "v3",
  "published": "2009-08-06T13:40:15.000Z",
  "updated": "2010-10-06T14:32:05.000Z",
  "title": "A pseudolocality theorem for Ricci flow",
  "authors": [
    "Shu-Yu Hsu"
  ],
  "comment": "11 pages, I have add one mild assumption on the theorem and completely rewrites the proof of the theorem which avoids the use of the logarithmic Sobolev inequality completely. I also obtain an extension of the compactness result of Hamilton on a sequence of complete pointed Riemannian manifolds evolving under Ricci flow",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper we will give a simple proof of a modification of a result on pseudolocality for the Ricci flow by P.Lu without using the pseudolocality theorem 10.1 of Perelman [P1]. We also obtain an extension of a result of Hamilton on the compactness of a sequence of complete pointed Riemannian manifolds $\\{(M_k,g_k(t),x_k)\\}_{k=1}^{\\infty}$ evolving under Ricci flow with uniform bounded sectional curvatures on $[0,T]$ and uniform positive lower bound on the injectivity radii at $x_k$ with respect to the metric $g_k(0)$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-10-06T14:32:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J35",
      "53C44",
      "35K55"
    ],
    "keywords": [
      "ricci flow",
      "pseudolocality theorem",
      "uniform positive lower bound",
      "uniform bounded sectional curvatures",
      "complete pointed riemannian manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.0869H"
    }
  }
}