{
  "id": "1901.07783",
  "version": "v1",
  "published": "2019-01-23T09:34:17.000Z",
  "updated": "2019-01-23T09:34:17.000Z",
  "title": "The mutual singularity of harmonic measure and Hausdorff measure of codimension smaller than one",
  "authors": [
    "Xavier Tolsa"
  ],
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "Let $\\Omega\\subset\\mathbb R^{n+1}$ be open and let $E\\subset \\partial\\Omega$ with $0<H^s(E)<\\infty$, for some $s\\in(n,n+1)$, satisfy a local capacity density condition. In this paper it is shown that the harmonic measure cannot be mutually absolutely continuous with $H^s$ on $E$. This answers a question of Azzam and Mourgoglou, who had proved the same result under the additional assumption that $\\Omega$ is a uniform domain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-23T09:34:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B15",
      "31B20"
    ],
    "keywords": [
      "harmonic measure",
      "hausdorff measure",
      "codimension smaller",
      "mutual singularity",
      "local capacity density condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}