{
  "id": "math/0102037",
  "version": "v1",
  "published": "2001-02-05T11:38:48.000Z",
  "updated": "2001-02-05T11:38:48.000Z",
  "title": "Minimal surfaces that attain equality in the Chern-Osserman inequality",
  "authors": [
    "Masatoshi Kokubu",
    "Masaaki Umehara",
    "Kotaro Yamada"
  ],
  "comment": "6 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In the previous paper, Takahasi and the authors generalized the theory of minimal surfaces in Euclidean n-space to that of surfaces with holomorphic Gauss map in certain class of non-compact symmetric spaces. It also includes the theory of constant mean curvature one surfaces in hyperbolic 3-space. Moreover, a Chern-Osserman type inequality for such surfaces was shown. Though its equality condition is not solved yet, the authors have noticed that the equality condition of the original Chern-Osserman inequality itself is not found in any literature except for the case n=3, in spite of its importance. In this paper, a simple geometric condition for minimal surfaces that attains equality in the Chern-Osserman inequality is given. The authors hope it will be a useful reference for readers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-02-05T11:38:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "53A07",
      "53C42"
    ],
    "keywords": [
      "minimal surfaces",
      "attain equality",
      "equality condition",
      "holomorphic gauss map",
      "original chern-osserman inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......2037K"
    }
  }
}