{
  "id": "0711.1236",
  "version": "v1",
  "published": "2007-11-08T10:39:14.000Z",
  "updated": "2007-11-08T10:39:14.000Z",
  "title": "Maximum principle and convergence of fundamental solutions for the Ricci flow",
  "authors": [
    "Shu-Yu Hsu"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper we will prove a maximum principle for the solutions of linear parabolic equation on complete non-compact manifolds with a time varying metric. We will prove the convergence of the Neumann Green function of the conjugate heat equation for the Ricci flow in $B_k\\times (0,T)$ to the minimal fundamental solution of the conjugate heat equation as $k\\to\\infty$. We will prove the uniqueness of the fundamental solution under some exponential decay assumption on the fundamental solution. We will also give a detail proof of the convergence of the fundamental solutions of the conjugate heat equation for a sequence of pointed Ricci flow $(M_k\\times (-\\alpha,0],x_k,g_k)$ to the fundamental solution of the limit manifold as $k\\to\\infty$ which was used without proof by Perelman in his proof of the pseudolocality theorem for Ricci flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-08T10:39:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J35",
      "53C43"
    ],
    "keywords": [
      "ricci flow",
      "maximum principle",
      "conjugate heat equation",
      "convergence",
      "neumann green function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.1236H"
    }
  }
}