{
  "id": "0907.2724",
  "version": "v2",
  "published": "2009-07-16T15:46:52.000Z",
  "updated": "2009-07-29T13:44:42.000Z",
  "title": "Existence of Good Sweepouts on Closed Manifolds",
  "authors": [
    "Longzhi Lin",
    "Lu Wang"
  ],
  "comment": "7 pages; added reference; corrected typos",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this note we establish estimates for the harmonic map heat flow from $S^1$ into a closed manifold, and use it to construct sweepouts with the following good property: each curve in the tightened sweepout, whose energy is close to the maximal energy of curves in the sweepout, is itself close to a closed geodesic.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-07-29T13:44:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C22",
      "53C44"
    ],
    "keywords": [
      "closed manifold",
      "harmonic map heat flow",
      "maximal energy",
      "construct sweepouts",
      "tightened sweepout"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.2724L"
    }
  }
}