{
  "id": "1302.6164",
  "version": "v3",
  "published": "2013-02-25T17:19:08.000Z",
  "updated": "2013-06-10T05:43:06.000Z",
  "title": "On the volume of the convex hull of two convex bodies",
  "authors": [
    "Ákos G. Horváth",
    "Z. Lángi"
  ],
  "comment": "9 pages, 3 figures",
  "doi": "10.1007/s00605-013-0526-x",
  "categories": [
    "math.MG"
  ],
  "abstract": "In this note we examine the volume of the convex hull of two congruent copies of a convex body in Euclidean $n$-space, under some subsets of the isometry group of the space. We prove inequalities for this volume if the two bodies are translates, or reflected copies of each other about a common point or a hyperplane containing it. In particular, we give a proof of a related conjecture of Rogers and Shephard.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-06-10T05:43:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A40",
      "52A38",
      "26B15"
    ],
    "keywords": [
      "convex hull",
      "convex body",
      "congruent copies",
      "common point",
      "isometry group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.6164H"
    }
  }
}