{
  "id": "1509.00546",
  "version": "v1",
  "published": "2015-09-02T02:25:52.000Z",
  "updated": "2015-09-02T02:25:52.000Z",
  "title": "A characterization of cut locus for $C^1$-hypersurfaces",
  "authors": [
    "Tatsuya Miura"
  ],
  "comment": "10 pages, 3 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $\\Omega$ be an open set in $\\mathbb{R}^n$ with $C^1$-boundary. Let $\\Sigma$ be the skeleton of $\\Omega$, that is, the set $\\Sigma$ consists of points where the distance function to $\\partial\\Omega$ is not differentiable. This paper characterizes the cut locus (ridge) $\\overline{\\Sigma}$, which is the closure of $\\Sigma$, by introducing the lower semicontinuous envelope of radius of curvature of the boundary $\\partial\\Omega$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-02T02:25:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B05",
      "53A05"
    ],
    "keywords": [
      "cut locus",
      "characterization",
      "hypersurfaces",
      "lower semicontinuous envelope",
      "open set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}