{
  "id": "1505.06167",
  "version": "v1",
  "published": "2015-05-22T18:17:46.000Z",
  "updated": "2015-05-22T18:17:46.000Z",
  "title": "Uniform domains with rectifiable boundaries and harmonic measure",
  "authors": [
    "Mihalis Mourgoglou"
  ],
  "comment": "13 pages. arXiv admin note: text overlap with arXiv:1410.2782 by other authors",
  "categories": [
    "math.CA"
  ],
  "abstract": "We assume that $\\Omega \\subset \\mathbb{R}^{d+1}$ is a uniform domain with lower $d$-Ahlfors-David regular rectifiable boundary so that $\\mathcal{H}^d|_{\\partial \\Omega}$ is Radon. We show the Hausdorff measure $\\mathcal{H}^d$ is absolutely continuous with respect to the harmonic measure $\\omega$ in $\\partial \\Omega$ apart from a set of $\\mathcal{H}^d$-measure zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-22T18:17:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31A15",
      "28A75",
      "28A78"
    ],
    "keywords": [
      "harmonic measure",
      "uniform domain",
      "ahlfors-david regular rectifiable boundary",
      "hausdorff measure",
      "measure zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150506167M"
    }
  }
}