{
  "id": "1612.04213",
  "version": "v1",
  "published": "2016-12-13T14:53:15.000Z",
  "updated": "2016-12-13T14:53:15.000Z",
  "title": "The arc metric on Teichmüller spaces of surfaces of infinite type with boundary",
  "authors": [
    "Qiyu Chen",
    "Lixin Liu"
  ],
  "comment": "31 pages, 20 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $X_{0}$ be a complete hyperbolic surface of infinite type with geodesic boundary which admits a countable pair of pants decomposition. As an application of the Basmajian identity for complete bordered hyperbolic surfaces of infinite type with limit sets of 1-dimensional measure zero, we define an asymmetric metric (which is called arc metric) on the quasiconformal Teichm\\\"uller space $\\mathcal{T}(X_{0})$ provided that $X_{0}$ satisfies a geometric condition. Furthermore, we construct several examples of hyperbolic surfaces of infinite type satisfying the geometric condition and discuss the relation between the Shiga's condition and the geometric condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-13T14:53:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32G15",
      "30F30",
      "30F60"
    ],
    "keywords": [
      "infinite type",
      "arc metric",
      "teichmüller spaces",
      "geometric condition",
      "complete hyperbolic surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}