{
  "id": "1010.4008",
  "version": "v1",
  "published": "2010-10-19T19:09:03.000Z",
  "updated": "2010-10-19T19:09:03.000Z",
  "title": "Hypersurfaces of constant curvature in Hyperbolic space",
  "authors": [
    "Bo Guan",
    "Joel Spruck"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that for a very general and natural class of curvature functions, the problem of finding a complete strictly convex hypersurface satisfying f({\\kappa}) = {\\sigma} over (0,1) with a prescribed asymptotic boundary {\\Gamma} at infinity has at least one solution which is a \"vertical graph\" over the interior (or the exterior) of {\\Gamma}. There is uniqueness for a certain subclass of these curvature functions and as {\\sigma} varies between 0 and 1, these hypersurfaces foliate the two components of the complement of the hyperbolic convex hull of {\\Gamma}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-19T19:09:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "35J65",
      "58J32"
    ],
    "keywords": [
      "hyperbolic space",
      "constant curvature",
      "curvature functions",
      "hyperbolic convex hull",
      "natural class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.4008G"
    }
  }
}