{
  "id": "1304.4295",
  "version": "v1",
  "published": "2013-04-15T23:34:12.000Z",
  "updated": "2013-04-15T23:34:12.000Z",
  "title": "Boundary blow up under Sobolev mappings",
  "authors": [
    "Aapo Kauranen",
    "Pekka Koskela"
  ],
  "comment": "11 pages, submitted",
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove that for mappings $W^{1,n}(B^n, \\R^n),$ continuous up to the boundary, with modulus of continuity satisfying certain divergence condition, the image of the boundary of the unit ball has zero $n$-Hausdorff measure. For H\\\"older continuous mappings we also prove an essentially sharp generalized Hausdorff dimension estimate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-15T23:34:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sobolev mappings",
      "boundary blow",
      "sharp generalized hausdorff dimension estimate",
      "essentially sharp generalized hausdorff dimension",
      "divergence condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.4295K"
    }
  }
}