{
  "id": "1810.09308",
  "version": "v1",
  "published": "2018-10-22T14:21:25.000Z",
  "updated": "2018-10-22T14:21:25.000Z",
  "title": "On the existence of closed $C^{1,1}$ curves of constant curvature",
  "authors": [
    "Daniel Ketover",
    "Yevgeny Liokumovich"
  ],
  "categories": [
    "math.DG",
    "math.DS",
    "math.SG"
  ],
  "abstract": "We show that on any Riemannian surface for each $0<c<\\infty$ there exists an immersed $C^{1,1}$ curve that is smooth and with curvature equal to $|c|$ away from a point. We give examples showing that, in general, the regularity of the curve obtained by our procedure cannot be improved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-22T14:21:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C42"
    ],
    "keywords": [
      "constant curvature",
      "riemannian surface",
      "curvature equal",
      "regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}