{
  "id": "math/0009246",
  "version": "v2",
  "published": "2000-09-29T15:00:41.000Z",
  "updated": "2000-10-04T14:03:44.000Z",
  "title": "Calabi flow in Riemann surfaces revisited: A new point of view",
  "authors": [
    "Xiuxiong Chen"
  ],
  "comment": "22 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we observe a set of functionals of metrics which are all decrease under the Calabi flow and have uniform lower bound along the flow, which give rise to a set of integral estimates on the curvature flow. Using these estimates, together with weak compactness we obtained in previous papers [8] and [10], we prove the long term existence and convergence of the Calabi flow. Thus give a new proof to Chruscial's theorem. The set of simple ideas of global integral estimates and concentration compactness should have further implications in other heat flow problems.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-10-04T14:03:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "calabi flow",
      "riemann surfaces",
      "uniform lower bound",
      "long term existence",
      "global integral estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......9246C"
    }
  }
}