{
  "id": "1306.1406",
  "version": "v1",
  "published": "2013-06-06T13:32:03.000Z",
  "updated": "2013-06-06T13:32:03.000Z",
  "title": "Convergence to equilibrium of gradient flows defined on planar curves",
  "authors": [
    "Matteo Novaga",
    "Shinya Okabe"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the evolution of open planar curves by the steepest descent flow of a geometric functional, under different boundary conditions. We prove that, if any set of stationary solutions with fixed energy is finite, then a solution of the flow converges to a stationary solution as time goes to infinity. We also present a few applications of this result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-06T13:32:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "35K55"
    ],
    "keywords": [
      "gradient flows",
      "convergence",
      "stationary solution",
      "equilibrium",
      "steepest descent flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.1406N"
    }
  }
}