{
  "id": "1301.0332",
  "version": "v2",
  "published": "2013-01-02T21:15:17.000Z",
  "updated": "2013-02-25T20:59:06.000Z",
  "title": "Meromorphic quadratic differentials with half-plane structures",
  "authors": [
    "Subhojoy Gupta"
  ],
  "comment": "46 pages, 23 figures. Some minor corrections in v2, and a clarification added in section 10",
  "categories": [
    "math.GT",
    "math.CV"
  ],
  "abstract": "We prove the existence of \"half-plane differentials\" with prescribed local data on any Riemann surface. These are meromorphic quadratic differentials with higher-order poles which have an associated singular flat metric isometric to a collection of euclidean half-planes glued by an interval-exchange map on their boundaries. The local data is associated with the poles and consists of the integer order, a non-negative real residue, and a positive real leading order term. This generalizes a result of Strebel for differentials with double-order poles, and associates metric spines with the Riemann surface.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-25T20:59:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30F30",
      "30F60"
    ],
    "keywords": [
      "meromorphic quadratic differentials",
      "half-plane structures",
      "real leading order term",
      "local data",
      "riemann surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}