{
  "id": "1505.06088",
  "version": "v1",
  "published": "2015-05-22T14:11:03.000Z",
  "updated": "2015-05-22T14:11:03.000Z",
  "title": "Rectifiability of harmonic measure in domains with porous boundaries",
  "authors": [
    "Jonas Azzam",
    "Mihalis Mourgoglou",
    "Xavier Tolsa"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "We show that if $n\\geq 2$, $\\Omega\\subset \\mathbb R^{n+1}$ is a connected domain with porous boundary, and $E\\subset \\partial\\Omega$ is a set of finite and positive Hausdorff $H^{n}$-measure upon which the harmonic measure $\\omega$ is absolutely continuous with respect to $H^{n}$, then $\\omega|_E$ is concentrated on an $n$-rectifiable set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-22T14:11:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31A15",
      "28A75",
      "42B20"
    ],
    "keywords": [
      "harmonic measure",
      "porous boundary",
      "rectifiability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150506088A"
    }
  }
}