{
  "id": "1509.06294",
  "version": "v1",
  "published": "2015-09-21T16:38:05.000Z",
  "updated": "2015-09-21T16:38:05.000Z",
  "title": "Rectifiability of harmonic measure",
  "authors": [
    "Jonas Azzam",
    "Steve Hofmann",
    "José María Martell",
    "Svitlana Mayboroda",
    "Mihalis Mourgoglou",
    "Xavier Tolsa",
    "Alexander Volberg"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1505.06088, arXiv:1507.04409",
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "In the present paper we prove that for any open connected set $\\Omega\\subset\\mathbb{R}^{n+1}$, $n\\geq 1$, and any $E\\subset \\partial \\Omega$ with $0<\\mathcal{H}^n(E)<\\infty$ absolute continuity of the harmonic measure $\\omega$ with respect to the Hausdorff measure on $E$ implies that $\\omega|_E$ is rectifiable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-21T16:38:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31A15",
      "31B15",
      "30C85",
      "42B37",
      "31B05",
      "35J08",
      "42B20",
      "28A75",
      "28A78"
    ],
    "keywords": [
      "harmonic measure",
      "rectifiability",
      "open connected set",
      "absolute continuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150906294A"
    }
  }
}