{
  "id": "1311.4012",
  "version": "v3",
  "published": "2013-11-16T02:34:25.000Z",
  "updated": "2015-03-15T17:09:58.000Z",
  "title": "Proof of the Log-Convex Density Conjecture",
  "authors": [
    "Gregory R. Chambers"
  ],
  "comment": "40 pages, 7 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "We completely characterize isoperimetric regions in R^n with density e^h, where h is convex, smooth, and radially symmetric. In particular, balls around the origin constitute isoperimetric regions of any given volume, proving the Log-Convex Density Conjecture due to Kenneth Brakke.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-13T01:29:17.000Z",
      "comment": "44 pages, 11 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-03-15T17:09:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q20",
      "53C17"
    ],
    "keywords": [
      "log-convex density conjecture",
      "origin constitute isoperimetric regions",
      "characterize isoperimetric regions",
      "kenneth brakke"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.4012C"
    }
  }
}