{
  "id": "1801.01812",
  "version": "v1",
  "published": "2018-01-05T16:08:17.000Z",
  "updated": "2018-01-05T16:08:17.000Z",
  "title": "Horospheres in Teichmüller space and mapping class group",
  "authors": [
    "Weixu Su",
    "Dong Tan"
  ],
  "comment": "23 pages",
  "categories": [
    "math.GT",
    "math.CV"
  ],
  "abstract": "We study the geometry of horospheres in Teichm\\\"uller space of Riemann surfaces of genus g with n punctures, where $3g-3+n\\geq 2$. We show that every $C^1$-diffeomorphism of Teichm\\\"uller space to itself that preserves horospheres is an element of the extended mapping class group. Using the relation between horospheres and metric balls, we obtain a new proof of Royden's Theorem that the isometry group of the Teichm\\\"uller metric is the extended mapping class group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-05T16:08:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32G15",
      "30F30",
      "30F60"
    ],
    "keywords": [
      "teichmüller space",
      "extended mapping class group",
      "riemann surfaces",
      "isometry group",
      "roydens theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}