{
  "id": "math/0607398",
  "version": "v3",
  "published": "2006-07-17T22:30:01.000Z",
  "updated": "2008-05-23T05:29:38.000Z",
  "title": "An isoperimetric inequality on the $\\ell_p$ balls",
  "authors": [
    "Sasha Sodin"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/07-AIHP121 the Annales de l'Institut Henri Poincar\\'e - Probabilit\\'es et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annales de l'Institut Henri Poincar\\'e - Probabilit\\'es et Statistiques 2008, Vol. 44, No. 2, 362-373",
  "doi": "10.1214/07-AIHP121",
  "categories": [
    "math.PR",
    "math.MG"
  ],
  "abstract": "The normalised volume measure on the $\\ell_p^n$ unit ball ($1\\leq p\\leq 2$) satisfies the following isoperimetric inequality: the boundary measure of a set of measure $a$ is at least $cn^{1/p}\\tilde{a}\\log^{1-1/p}(1/\\tilde{a})$, where $\\tilde{a}=\\min(a,1-a)$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-05-23T05:29:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "isoperimetric inequality",
      "normalised volume measure",
      "unit ball"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008AnIHP..44..362S"
    }
  }
}