{
  "id": "1708.01510",
  "version": "v1",
  "published": "2017-08-03T12:00:45.000Z",
  "updated": "2017-08-03T12:00:45.000Z",
  "title": "A ball characterization in spaces of constant curvature",
  "authors": [
    "J. Jerónimo-Castro",
    "E. Makai Jr"
  ],
  "comment": "30 pages. arXiv admin note: text overlap with arXiv:1601.04494",
  "categories": [
    "math.MG"
  ],
  "abstract": "High proved the following theorem. If the intersections of any two congruent copies of a plane convex body are centrally symmetric, then this body is a circle. In our paper we extend the theorem of High to spherical, Euclidean and hyperbolic spaces, under some regularity assumptions. If in any of these spaces there is a pair of closed convex sets of class $C^2_+$ with interior points, different from the whole space, and the intersections of any congruent copies of these sets are centrally symmetric, then our sets are congruent balls.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-03T12:00:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A55",
      "52A20"
    ],
    "keywords": [
      "constant curvature",
      "ball characterization",
      "congruent copies",
      "plane convex body",
      "centrally symmetric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}