{
  "id": "0904.0978",
  "version": "v2",
  "published": "2009-04-06T17:53:39.000Z",
  "updated": "2009-04-19T00:47:25.000Z",
  "title": "Local solution and extension to the Calabi flow",
  "authors": [
    "Weiyong He"
  ],
  "comment": "11 pages; Proof of Theorem 2.1 is rewritten",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We consider the local solution to the Calabi flow for C^\\alpha initial metric. We also prove that the Calabi flow on compact Kaehler surfaces can be extended once the metrics along the flow are bounded in L^\\infty sense. This can be viewed as obtaining higher order derivative estimates from second order derivatives for a fourth order nonlinear equation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-04-19T00:47:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "calabi flow",
      "local solution",
      "fourth order nonlinear equation",
      "obtaining higher order derivative estimates",
      "compact kaehler surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.0978H"
    }
  }
}