{
  "id": "math/0701153",
  "version": "v2",
  "published": "2007-01-05T07:46:07.000Z",
  "updated": "2007-02-24T01:08:01.000Z",
  "title": "Pseudolocality for the Ricci flow and applications",
  "authors": [
    "Albert Chau",
    "Luen-Fai Tam",
    "Chengjie Yu"
  ],
  "comment": "44 pages; added Corollary to Theorem 1.1; correction to Theorem 8.1",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In \\cite{P1}, Perelman established a differential Li-Yau-Hamilton (LYH) type inequality for fundamental solutions of the conjugate heat equation corresponding to the Ricci flow on compact manifolds (also see \\cite{N2}). As an application of the LYH inequality, Perelman proved a pseudolocality result for the Ricci flow on compact manifolds. In this article we provide the details for the proofs of these results in the case of a complete non-compact Riemannian manifold. Using these results we prove that under certain conditions, a finite time singularity of the Ricci flow must form within a compact set. We also prove a long time existence result for the \\KRF flow on complete non-negatively curved \\K manifolds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-02-24T01:08:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44"
    ],
    "keywords": [
      "ricci flow",
      "pseudolocality",
      "application",
      "long time existence result",
      "compact manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1153C"
    }
  }
}