{
  "id": "1601.02840",
  "version": "v1",
  "published": "2016-01-12T13:06:02.000Z",
  "updated": "2016-01-12T13:06:02.000Z",
  "title": "The Gradient Flow of O'Hara's Knot Energies",
  "authors": [
    "Simon Blatt"
  ],
  "comment": "45 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Jun O'Hara invented a family of knot energies $E^{j,p}$, $j,p \\in (0, \\infty)$. We study the negative gradient flow of the sum of one of the energies $E^\\alpha = E^{\\alpha,1}$, $\\alpha \\in (2,3)$, and a positive multiple of the length. Showing that the gradients of these knot energies can be written as the normal part of a quasilinear operator, we derive short time existence results for these flows. We then prove long time existence and convergence to critical points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-12T13:06:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "35S10"
    ],
    "keywords": [
      "oharas knot energies",
      "derive short time existence results",
      "long time existence",
      "quasilinear operator",
      "normal part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160102840B"
    }
  }
}