{
  "id": "1306.6688",
  "version": "v3",
  "published": "2013-06-28T01:09:29.000Z",
  "updated": "2014-11-11T18:05:37.000Z",
  "title": "Ricci flow on surfaces with conic singularities",
  "authors": [
    "Rafe Mazzeo",
    "Yanir A. Rubinstein",
    "Natasa Sesum"
  ],
  "comment": "v1: 38 pages v2: 39 pages, restructured Sections 1 and 2, and added references and Subsection 5.4. v3: 42 pages, revised to address referee comments; original proof of Proposition 5.3 had an error pointed out to us by a referee. We fix this by invoking Hamilton's original argument instead of the Hamilton compactness theorem",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We establish the short-time existence of the Ricci flow on surfaces with a finite number of conic points, all with cone angle between 0 and $2\\pi$, where the cone angles remain fixed or change in some smooth prescribed way. For the angle-preserving flow we prove long-time existence and convergence. When the Troyanov angle condition is satisfied (equivalently, when the data is logarithmically K-stable), the flow converges to the unique constant curvature metric with the given cone angles; if this condition is not satisfied, the flow converges subsequentially to a soliton. This is the one-dimensional version of the Hamilton--Tian conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-30T15:30:23.000Z",
      "comment": "v1: 38 pages v2: 39 pages, restructured Sections 1 and 2, and added references and Subsection 5.4",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-11-11T18:05:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "53C25"
    ],
    "keywords": [
      "ricci flow",
      "conic singularities",
      "unique constant curvature metric",
      "flow converges",
      "troyanov angle condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.6688M"
    }
  }
}