{
  "id": "1105.2719",
  "version": "v1",
  "published": "2011-05-13T13:17:48.000Z",
  "updated": "2011-05-13T13:17:48.000Z",
  "title": "Two isoperimetric inequalities for the Sobolev constant",
  "authors": [
    "Tom Carroll",
    "Jesse Ratzkin"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this note we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first such inequality is a variation on the classical Schwarz Lemma from complex analysis, similar to recent inequalities of Burckel, Marshall, Minda, Poggi-Corradini, and Ransford, while the second generalises an isoperimetric inequality for the first eigenfunction of the Laplacian due to Payne and Rayner.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-13T13:17:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "isoperimetric inequality",
      "sobolev constant",
      "associated extremal function",
      "classical schwarz lemma",
      "complex analysis"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00033-012-0198-8",
      "journal": "Zeitschrift Angewandte Mathematik und Physik",
      "year": 2012,
      "month": "Oct",
      "volume": 63,
      "number": 5,
      "pages": 855
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012ZaMP...63..855C"
    }
  }
}