{
  "id": "1911.07797",
  "version": "v1",
  "published": "2019-11-18T17:52:39.000Z",
  "updated": "2019-11-18T17:52:39.000Z",
  "title": "The conformal measures of a normal subgroup of a cocompact Fuchsian group",
  "authors": [
    "Ofer Shwartz"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we study the conformal measures of a normal subgroup of a cocompact Fuchsian group. In particular, we relate the extremal conformal measures to the eigenmeasures of a suitable Ruelle operator. Using Ancona's theorem, adapted to the Ruelle operator setting, we show that if the group of deck transformations $G$ is hyperbolic then the extremal conformal measures and the hyperbolic boundary of $G$ coincide. We then interpret these results in terms of the asymptotic behavior of cutting sequences of geodesics on a regular cover of a compact hyperbolic surface.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-18T17:52:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F67",
      "30F35",
      "31C35",
      "37D40"
    ],
    "keywords": [
      "cocompact fuchsian group",
      "normal subgroup",
      "extremal conformal measures",
      "ruelle operator",
      "compact hyperbolic surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}