{
  "id": "1503.08083",
  "version": "v1",
  "published": "2015-03-27T14:06:31.000Z",
  "updated": "2015-03-27T14:06:31.000Z",
  "title": "On the asymptotic Plateau problem for CMC hypersurfaces in hyperbolic space",
  "authors": [
    "Jaime Ripoll",
    "Miriam Telichevesky"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1309.3644",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $\\mathbb{R}_{+}^{n+1}$ \\ be the half-space model of the hyperbolic space $\\mathbb{H}^{n+1}.$ It is proved that if $\\Gamma\\subset\\left\\{ x_{n+1}=0\\right\\} \\subset\\partial_{\\infty}\\mathbb{H}^{n+1}$ is a bounded $C^{0}$ Euclidean graph over $\\left\\{ x_{1}=0,\\text{ }x_{n+1}=0\\right\\} $ then, given $\\left\\vert H\\right\\vert <1,$ there is a complete, properly embedded, CMC $H$ hypersurface $\\Sigma$ of $\\mathbb{H}^{n+1}$ such that $\\partial_{\\infty }S=\\Gamma\\cup\\left\\{ x_{n+1}=+\\infty\\right\\} .$ This result can be seen as a limit case of the existence theorem proved by B. Guan and J. Spruck in \\cite{GS} on CMC $\\left\\vert H\\right\\vert <1$ radial graphs with prescribed $C^{0}$ asymptotic boundary data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-27T14:06:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic plateau problem",
      "hyperbolic space",
      "cmc hypersurfaces",
      "asymptotic boundary data",
      "euclidean graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}