{
  "id": "1610.07409",
  "version": "v1",
  "published": "2016-10-24T13:43:58.000Z",
  "updated": "2016-10-24T13:43:58.000Z",
  "title": "Coarse and fine geometry of the Thurston metric",
  "authors": [
    "David Dumas",
    "Anna Lenzhen",
    "Kasra Rafi",
    "Jing Tao"
  ],
  "comment": "40 pages, 11 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We study the geometry of the Thurston metric on the Teichm\\\"uller space $\\mathcal{T}(S)$ of hyperbolic structures on a surface $S$. Some of our results on the coarse geometry of this metric apply to arbitrary surfaces $S$ of finite type; however, we focus particular attention on the case where the surface is a once-punctured torus, $S_{1,1}$. In that case, our results provide a detailed picture of the infinitesimal, local, and global behavior of the geodesics of the Thurston metric, as well as an analogue of Royden's theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-24T13:43:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30F60",
      "57M50"
    ],
    "keywords": [
      "thurston metric",
      "fine geometry",
      "global behavior",
      "hyperbolic structures",
      "finite type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}