{
  "id": "math/0204027",
  "version": "v1",
  "published": "2002-04-02T09:23:52.000Z",
  "updated": "2002-04-02T09:23:52.000Z",
  "title": "Painleve's problem and the semiadditivity of analytic capacity",
  "authors": [
    "Xavier Tolsa"
  ],
  "comment": "42 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $\\gamma(E)$ be the analytic capacity of a compact set $E$ and let $\\gamma_+(E)$ be the capacity of $E$ originated by Cauchy transforms of positive measures. In this paper we prove that $\\gamma(E)\\approx\\gamma_+(E)$ with estimates independent of $E$. As a corollary, we characterize removable singularities for bounded analytic functions in terms of curvature of measures, and we deduce that $\\gamma$ is semiadditive, which solves a long standing question of Vitushkin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-04-02T09:23:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C85",
      "42B20"
    ],
    "keywords": [
      "analytic capacity",
      "painleves problem",
      "semiadditivity",
      "long standing question",
      "compact set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......4027T"
    }
  }
}