{
  "id": "1202.3860",
  "version": "v2",
  "published": "2012-02-17T10:02:32.000Z",
  "updated": "2012-11-27T14:17:45.000Z",
  "title": "Uniform rectifiability and harmonic measure II: Poisson kernels in $L^p$ imply uniform rectifiability",
  "authors": [
    "Steve Hofmann",
    "José María Martell",
    "Ignacio Uriarte-Tuero"
  ],
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "We present the converse to a higher dimensional, scale-invariant version of a classical theorem of F. and M. Riesz. More precisely, for $n\\geq 2$, for an ADR domain $\\Omega\\subset \\re^{n+1}$ which satisfies the Harnack Chain condition plus an interior (but not exterior) Corkscrew condition, we show that absolute continuity of harmonic measure with respect to surface measure on $\\partial\\Omega$, with scale invariant higher integrability of the Poisson kernel, is sufficient to imply uniformly rectifiable of $\\partial\\Omega$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-27T14:17:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B05",
      "35J08",
      "35J25",
      "42B99",
      "42B25",
      "42B37"
    ],
    "keywords": [
      "imply uniform rectifiability",
      "harmonic measure",
      "poisson kernel",
      "harnack chain condition plus",
      "scale invariant higher integrability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.3860H"
    }
  }
}