{
  "id": "math/9211216",
  "version": "v1",
  "published": "1992-11-01T00:00:00.000Z",
  "updated": "1992-11-01T00:00:00.000Z",
  "title": "A low-technology estimate in convex geometry",
  "authors": [
    "Greg Kuperberg"
  ],
  "comment": "The abstract is adapted from the Math Review by Keith Ball, MR 93h:52010",
  "journal": "Internat. Math. Res. Notices, 1992 (1992), no. 9, 181-183",
  "categories": [
    "math.MG",
    "math.FA"
  ],
  "abstract": "Let $K$ be an $n$-dimensional symmetric convex body with $n \\ge 4$ and let $K\\dual$ be its polar body. We present an elementary proof of the fact that $$(\\Vol K)(\\Vol K\\dual)\\ge \\frac{b_n^2}{(\\log_2 n)^n},$$ where $b_n$ is the volume of the Euclidean ball of radius 1. The inequality is asymptotically weaker than the estimate of Bourgain and Milman, which replaces the $\\log_2 n$ by a constant. However, there is no known elementary proof of the Bourgain-Milman theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1992-11-01T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex geometry",
      "low-technology estimate",
      "elementary proof",
      "dimensional symmetric convex body",
      "bourgain-milman theorem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1992math.....11216K"
    }
  }
}