{
  "id": "1108.1641",
  "version": "v4",
  "published": "2011-08-08T09:10:42.000Z",
  "updated": "2015-05-28T03:37:15.000Z",
  "title": "Constant mean curvature surfaces in hyperbolic 3-space via loop groups",
  "authors": [
    "Josef F. Dorfmeister",
    "Jun-ichi Inoguchi",
    "Shimpei Kobayashi"
  ],
  "comment": "37 pages, 4 figures. v3: Various typos fixed. v4: Proposition D.1 has been fixed",
  "categories": [
    "math.DG"
  ],
  "abstract": "In hyperbolic 3-space $\\mathbb{H}^3$ surfaces of constant mean curvature $H$ come in three types, corresponding to the cases $0 \\leq H < 1$, $H = 1$, $H > 1$. Via the Lawson correspondence the latter two cases correspond to constant mean curvature surfaces in Euclidean 3-space $\\mathbb{E}^3$ with H=0 and $H \\neq 0$, respectively. These surface classes have been investigated intensively in the literature. For the case $0 \\leq H < 1$ there is no Lawson correspondence in Euclidean space and there are relatively few publications. Examples have been difficult to construct. In this paper we present a generalized Weierstra{\\ss} type representation for surfaces of constant mean curvature in $\\mathbb{H}^3$ with particular emphasis on the case of mean curvature $0\\leq H < 1$. In particular, the generalized Weierstra{\\ss} type representation presented in this paper enables us to construct simultaneously minimal surfaces (H=0) and non-minimal constant mean curvature surfaces ($0<H<1$).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-08-12T01:42:33.000Z",
      "comment": "37 pages, 4 figures. v3: Various typos fixed",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-05-28T03:37:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "loop groups",
      "non-minimal constant mean curvature surfaces",
      "hyperbolic",
      "type representation",
      "lawson correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.1641D"
    }
  }
}