{
  "id": "1107.5406",
  "version": "v4",
  "published": "2011-07-27T08:09:21.000Z",
  "updated": "2012-05-17T17:53:19.000Z",
  "title": "Weighted isoperimetric inequalities in cones and applications",
  "authors": [
    "Friedemann Brock",
    "Francesco Chiacchio",
    "Anna Mercaldo"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper deals with weighted isoperimetric inequalities relative to cones of $\\mathbb{R}^{N}$. We study the structure of measures that admit as isoperimetric sets the intersection of a cone with balls centered at the vertex of the cone. For instance, in case that the cone is the half-space $\\mathbb{R}_{+}^{N}={x \\in \\mathbb{R}^{N} : x_{N}>0}$ and the measure is factorized, we prove that this phenomenon occurs if and only if the measure has the form $d\\mu=ax_{N}^{k}\\exp(c|x|^{2})dx $, for some $a>0$, $k,c\\geq 0$. Our results are then used to obtain isoperimetric estimates for Neumann eigenvalues of a weighted Laplace-Beltrami operator on the sphere, sharp Hardy-type inequalities for functions defined in a quarter space and, finally, via symmetrization arguments, a comparison result for a class of degenerate PDE's.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-05-17T17:53:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D20",
      "35J70",
      "46E35"
    ],
    "keywords": [
      "weighted isoperimetric inequalities",
      "applications",
      "sharp hardy-type inequalities",
      "comparison result",
      "symmetrization arguments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.5406B"
    }
  }
}