{
  "id": "1403.3236",
  "version": "v1",
  "published": "2014-03-13T11:31:21.000Z",
  "updated": "2014-03-13T11:31:21.000Z",
  "title": "Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature",
  "authors": [
    "Julià Cufí",
    "Agustí Reventós"
  ],
  "comment": "16 pages, 3 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "We relate the total curvature and the isoperimetric deficit of a curve $\\gamma$ in a two-dimensional space of constant curvature with the area enclosed by the evolute of $\\gamma$. We provide also a Gauss-Bonnet theorem for a special class of evolutes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-13T11:31:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A04"
    ],
    "keywords": [
      "constant curvature",
      "isoperimetric deficit",
      "two-dimensional space",
      "special class",
      "gauss-bonnet theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.3236C"
    }
  }
}