{
  "id": "1612.08043",
  "version": "v1",
  "published": "2016-12-23T17:17:05.000Z",
  "updated": "2016-12-23T17:17:05.000Z",
  "title": "Meromorphic quadratic differentials and measured foliations on a Riemann surface",
  "authors": [
    "Subhojoy Gupta",
    "Michael Wolf"
  ],
  "comment": "46 pages, 8 figures; for completeness, some adaptations of earlier arguments of the authors are provided in the Appendices",
  "categories": [
    "math.GT",
    "math.CV"
  ],
  "abstract": "We describe the space of measured foliations induced on a compact Riemann surface by meromorphic quadratic differentials. We prove that any such foliation is realized by a unique such differential $q$ if we prescribe, in addition, the principal parts of $\\sqrt q$ at the poles. This generalizes a theorem of Hubbard and Masur for holomorphic quadratic differentials. The proof analyzes infinite-energy harmonic maps from the Riemann surface to $\\mathbb{R}$-trees of infinite co-diameter, with prescribed behavior at the poles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-23T17:17:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30F30",
      "30F60"
    ],
    "keywords": [
      "meromorphic quadratic differentials",
      "measured foliations",
      "proof analyzes infinite-energy harmonic maps",
      "holomorphic quadratic differentials",
      "compact riemann surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}