{
  "id": "1904.13129",
  "version": "v1",
  "published": "2019-04-30T09:58:50.000Z",
  "updated": "2019-04-30T09:58:50.000Z",
  "title": "On the regularity of critical points for O'Hara's knot energies: From smoothness to analyticity",
  "authors": [
    "Nicole Vorderobermeier"
  ],
  "categories": [
    "math.AP",
    "math.GT"
  ],
  "abstract": "We prove the analyticity of smooth critical points for O'Hara's knot energies $\\mathcal{E}^{\\alpha,p}$, with $p=1$ and $2<\\alpha< 3$, subject to a fixed length constraint. This implies, together with the main result in \\cite{BR13}, that bounded energy critical points of $\\mathcal{E}^{\\alpha,1}$ subject to a fixed length constraint are not only $C^\\infty$ but also analytic. Our approach is based on Cauchy's method of majorants and a decomposition of the gradient that was adapted from the M\\\"obius energy case $\\mathcal{E}^{2,1}$ in \\cite{BV19}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-30T09:58:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "57M25"
    ],
    "keywords": [
      "oharas knot energies",
      "analyticity",
      "fixed length constraint",
      "smoothness",
      "regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}