{
  "id": "1203.5739",
  "version": "v1",
  "published": "2012-03-26T17:38:28.000Z",
  "updated": "2012-03-26T17:38:28.000Z",
  "title": "Convex Spacelike Hypersurfaces of Constant Curvature in de Sitter Space",
  "authors": [
    "Joel Spruck",
    "Ling Xiao"
  ],
  "comment": "24 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We show that for a very general and natural class of curvature functions (for example the curvature quotients $(\\sigma_n/\\sigma_l)^{\\frac{1}{n-l}}$) the problem of finding a complete spacelike strictly convex hypersurface in de Sitter space satisfying $f(\\kappa) = \\sigma \\in (1,\\infty)$ with a prescribed compact future asymptotic boundary $\\Gamma$ at infinity has at least one smooth solution (if l = 1 or l = 2 there is uniqueness). This is the exact analogue of the asymptotic plateau problem in Hyperbolic space and is in fact a precise dual problem. By using this duality we obtain for free the existence of strictly convex solutions to the asymptotic Plateau problem for $\\sigma_l = \\sigma$; $1\\leq l < n$ in both deSitter and Hyperbolic space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-26T17:38:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "35J65",
      "58J32"
    ],
    "keywords": [
      "convex spacelike hypersurfaces",
      "sitter space",
      "constant curvature",
      "asymptotic plateau problem",
      "hyperbolic space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.5739S"
    }
  }
}