{
  "id": "1912.03856",
  "version": "v1",
  "published": "2019-12-09T05:42:09.000Z",
  "updated": "2019-12-09T05:42:09.000Z",
  "title": "Equidistribution of horospheres on moduli spaces of hyperbolic surfaces",
  "authors": [
    "Francisco Arana-Herrera"
  ],
  "comment": "41 pages",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "Given a simple closed curve $\\gamma$ on a connected, oriented, closed surface $S$ of negative Euler characteristic, Mirzakhani showed that the set of points in the moduli space of hyperbolic structures on $S$ having a simple closed geodesic of length $L$ of the same topological type as $\\gamma$ equidistributes with respect to a natural probability measure as $L \\to \\infty$. We prove several generalizations of Mirzakhani's result and discuss some of the technical aspects ommited in her original work. The dynamics of the earthquake flow play a fundamental role in the arguments in this paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-09T05:42:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli space",
      "hyperbolic surfaces",
      "equidistribution",
      "horospheres",
      "natural probability measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}