{
  "id": "1912.00880",
  "version": "v1",
  "published": "2019-12-02T15:58:03.000Z",
  "updated": "2019-12-02T15:58:03.000Z",
  "title": "Measure comparison and distance inequalities for convex bodies",
  "authors": [
    "Alexander Koldobsky",
    "Grigoris Paouris",
    "Artem Zvavitch"
  ],
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show how these results can be used to recover slicing and distance inequalities. We also prove a sharp upper estimate for the outer volume ratio distance from an arbitrary convex body to the unit balls of subspaces of $L_p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-02T15:58:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "53A15",
      "52B10"
    ],
    "keywords": [
      "distance inequalities",
      "measure comparison",
      "outer volume ratio distance",
      "sharp upper estimate",
      "arbitrary convex body"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}