{
  "id": "1601.02925",
  "version": "v1",
  "published": "2016-01-12T15:49:25.000Z",
  "updated": "2016-01-12T15:49:25.000Z",
  "title": "Sharp Poincaré-type inequality for the Gaussian measure on the boundary of convex sets",
  "authors": [
    "Alexander V. Kolesnikov",
    "Emanuel Milman"
  ],
  "comment": "13 pages",
  "categories": [
    "math.FA",
    "math.PR"
  ],
  "abstract": "A sharp Poincar\\'e-type inequality is derived for the restriction of the Gaussian measure on the boundary of a convex set. In particular, it implies a Gaussian mean-curvature inequality and a Gaussian iso second-variation inequality. The new inequality is nothing but an infinitesimal form of Ehrhard's inequality for the Gaussian measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-12T15:49:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian measure",
      "sharp poincaré-type inequality",
      "convex set",
      "gaussian iso second-variation inequality",
      "sharp poincare-type inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160102925K"
    }
  }
}