{
  "id": "1009.3583",
  "version": "v1",
  "published": "2010-09-18T21:09:50.000Z",
  "updated": "2010-09-18T21:09:50.000Z",
  "title": "A note on Mahler's conjecture",
  "authors": [
    "Shlomo Reisner",
    "Carsten Schütt",
    "Elisabeth M. Werner"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $K$ be a convex body in $\\mathbb{R}^n$ with Santal\\'o point at 0\\. We show that if $K$ has a point on the boundary with positive generalized Gau{\\ss} curvature, then the volume product $|K| |K^\\circ|$ is not minimal. This means that a body with minimal volume product has Gau{\\ss} curvature equal to 0 almost everywhere and thus suggests strongly that a minimal body is a polytope.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-18T21:09:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20"
    ],
    "keywords": [
      "mahlers conjecture",
      "minimal volume product",
      "santalo point",
      "minimal body",
      "convex body"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.3583R"
    }
  }
}