{
  "id": "math/0008007",
  "version": "v1",
  "published": "2000-08-01T11:27:17.000Z",
  "updated": "2000-08-01T11:27:17.000Z",
  "title": "Inequalities for the Gamma Function and estimates for the volume of sections of $B_p^n$",
  "authors": [
    "Jesus Bastero",
    "Fernando Galve",
    "Ana Pena",
    "Miguel Romance"
  ],
  "comment": "10 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We consider $k$-dimensional central sections of the unit ball of $\\ell_p^n$ (denoted $B_p^n$) and we prove that their volume are bounded by the volume of $B_p^n$ whenever $1<p<2$ and $1\\le k\\le (n-1)/2$ or $k=n-1$. We also consider $0<p<1$ and other cases. We obtain sharp inequalities involving Gamma Function in order to get these results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-08-01T11:27:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "33B15",
      "46B20"
    ],
    "keywords": [
      "gamma function",
      "dimensional central sections",
      "sharp inequalities",
      "unit ball"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......8007B"
    }
  }
}