{
  "id": "1708.03289",
  "version": "v1",
  "published": "2017-08-10T16:34:09.000Z",
  "updated": "2017-08-10T16:34:09.000Z",
  "title": "Double Bubbles on the Real Line with Log-Convex Density",
  "authors": [
    "Eliot Bongiovanni",
    "Leonardo Di Giosia",
    "Alejandro Diaz",
    "Jahangir Habib",
    "Arjun Kakkar",
    "Lea Kenigsberg",
    "Dylanger Pittman",
    "Nat Sothanaphan",
    "Weitao Zhu"
  ],
  "comment": "44 pages, 10 figures",
  "categories": [
    "math.MG",
    "math.DG"
  ],
  "abstract": "The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in $\\mathbb{R}^N$ is the standard double bubble. We seek the optimal double bubble in $\\mathbb{R}^N$ with density, which we assume to be strictly log-convex. For $N=1$ we show that the solution is sometimes two contiguous intervals and sometimes three contiguous intervals. In higher dimensions, we think that the solution is sometimes a standard double bubble and sometimes concentric spheres (e.g. for one volume small and the other large).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-10T16:34:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q10"
    ],
    "keywords": [
      "real line",
      "log-convex density",
      "classic double bubble theorem says",
      "standard double bubble",
      "contiguous intervals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}