{
  "id": "math/0602135",
  "version": "v1",
  "published": "2006-02-07T16:24:51.000Z",
  "updated": "2006-02-07T16:24:51.000Z",
  "title": "On the isoperimetric problem in Euclidean space with density",
  "authors": [
    "César Rosales",
    "Antonio Cañete",
    "Vincent Bayle",
    "Frank Morgan"
  ],
  "comment": "19 pages, 3 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive stability conditions, which lead to the conjecture that for a radial log-convex density, balls about the origin are isoperimetric regions. Finally, we prove this conjecture and the uniqueness of minimizers for the density $\\exp (|x|^2)$ by using symmetrization techniques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-02-07T16:24:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q20",
      "53C17"
    ],
    "keywords": [
      "euclidean space",
      "isoperimetric problem",
      "radial log-convex density",
      "existence results",
      "characterize isoperimetric regions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2135R"
    }
  }
}