{
  "id": "1403.7158",
  "version": "v2",
  "published": "2014-03-27T18:13:50.000Z",
  "updated": "2014-05-07T19:33:15.000Z",
  "title": "Affine diameters of convex bodies",
  "authors": [
    "Imre Barany",
    "Daniel Hug",
    "Rolf Schneider"
  ],
  "comment": "Minor corrections",
  "categories": [
    "math.MG"
  ],
  "abstract": "We prove sharp inequalities for the average number of affine diameters through the points of a convex body $K$ in ${\\mathbb R}^n$. These inequalities hold if $K$ is either a polytope or of dimension two. An example shows that the proof given in the latter case does not extend to higher dimensions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-07T19:33:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "52A40"
    ],
    "keywords": [
      "convex body",
      "affine diameters",
      "higher dimensions",
      "average number",
      "inequalities hold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.7158B"
    }
  }
}