{
  "id": "2301.04084",
  "version": "v1",
  "published": "2023-01-10T17:18:00.000Z",
  "updated": "2023-01-10T17:18:00.000Z",
  "title": "The dimension of harmonic measure on some AD-regular flat sets of fractional dimension",
  "authors": [
    "Xavier Tolsa"
  ],
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "In this paper it is shown that if $E\\subset\\mathbb R^{n+1}$ is an $s$-AD regular compact set, with $s\\in [n-\\frac12,n)$, and $E$ is contained in a hyperplane or, more generally, in an $n$-dimensional $C^1$ manifold, then the Hausdorff dimension of the harmonic measure for the domain $\\mathbb R^{n+1}\\setminus E$ is strictly smaller than $s$, i.e., than the Hausdorff dimension of $E$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-10T17:18:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B15",
      "31B20"
    ],
    "keywords": [
      "ad-regular flat sets",
      "harmonic measure",
      "fractional dimension",
      "hausdorff dimension",
      "ad regular compact set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}