{
  "id": "1004.1484",
  "version": "v4",
  "published": "2010-04-09T07:46:04.000Z",
  "updated": "2012-05-21T05:30:16.000Z",
  "title": "Value distribution of the Gauss map of improper affine spheres",
  "authors": [
    "Yu Kawakami",
    "Daisuke Nakajo"
  ],
  "comment": "20 pages, no figure, to appear in Journal of the Mathematical Society of Japan",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "We give the best possible upper bound for the number of exceptional values of the Lagrangian Gauss map of complete improper affine fronts in the affine three-space. We also obtain the sharp estimate for weakly complete case. As an application of this result, we provide a new and simple proof of the parametric affine Bernstein problem for improper affine spheres. Moreover we get the same estimate for the ratio of canonical forms of weakly complete flat fronts in hyperbolic three-space.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-05-21T05:30:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A15",
      "30D35",
      "53A35",
      "53C42"
    ],
    "keywords": [
      "improper affine spheres",
      "value distribution",
      "complete improper affine fronts",
      "parametric affine bernstein problem",
      "weakly complete flat fronts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.1484K"
    }
  }
}