{
  "id": "1110.3110",
  "version": "v3",
  "published": "2011-10-14T02:09:03.000Z",
  "updated": "2013-08-09T12:36:28.000Z",
  "title": "A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic three-space",
  "authors": [
    "Yu Kawakami"
  ],
  "comment": "11 pages, no figure, to appear in Geometriae Dedicata. arXiv admin note: substantial text overlap with arXiv:1004.1484",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "We provide an effective ramification theorem for the ratio of canonical forms of a weakly complete flat front in the hyperbolic three-space. Moreover we give the two applications of this theorem, the first one is to show an analogue of the Ahlfors islands theorem for it and the second one is to give a simple proof of the classification of complete nonsingular flat surfaces in the hyperbolic three-space.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-08-09T12:36:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30D35",
      "53A35",
      "53C42"
    ],
    "keywords": [
      "hyperbolic three-space",
      "canonical forms",
      "complete nonsingular flat surfaces",
      "ahlfors islands theorem",
      "weakly complete flat front"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.3110K"
    }
  }
}