{
  "id": "0705.3012",
  "version": "v1",
  "published": "2007-05-21T16:30:44.000Z",
  "updated": "2007-05-21T16:30:44.000Z",
  "title": "Curve shortening and the topology of closed geodesics on surfaces",
  "authors": [
    "Sigurd B. Angenent"
  ],
  "comment": "55 pages, published version",
  "journal": "Ann. of Math. (2) 162 (2005), no. 3, 1187--1241",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study \"flat knot types\" of geodesics on compact surfaces M^2. For every flat knot type and any Riemannian metric g we introduce a Conley index associated with the curve shortening flow on the space of immersed curves on M^2. We conclude existence of closed geodesics with prescribed flat knot types, provided the associated Conley index is nontrivial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-21T16:30:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "53C22",
      "58E10"
    ],
    "keywords": [
      "closed geodesics",
      "prescribed flat knot types",
      "riemannian metric",
      "curve shortening flow",
      "conclude existence"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.3012A"
    }
  }
}