{
  "id": "1406.0813",
  "version": "v1",
  "published": "2014-06-03T18:41:00.000Z",
  "updated": "2014-06-03T18:41:00.000Z",
  "title": "On the average number of normals through points of a convex body",
  "authors": [
    "Gábor Domokos",
    "Zsolt Lángi"
  ],
  "comment": "15 pages",
  "categories": [
    "math.MG"
  ],
  "abstract": "In 1944, Santal\\'o asked about the average number of normals through a point of a given convex body. Since then, numerous results appeared in the literature about this problem. The aim of this paper is to give a concise summary of these results, with some new, recent developments. We point out connections of this problem to static equilibria of rigid bodies as well as to geometric partial differential equations of surface evolution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-03T18:41:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A40",
      "52A20",
      "28A75"
    ],
    "keywords": [
      "average number",
      "convex body",
      "geometric partial differential equations",
      "static equilibria",
      "rigid bodies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.0813D"
    }
  }
}