{
  "id": "2104.09751",
  "version": "v1",
  "published": "2021-04-20T04:04:27.000Z",
  "updated": "2021-04-20T04:04:27.000Z",
  "title": "Smooth Solutions to the Asymptotic Plateau Problem in Hyperbolic Space",
  "authors": [
    "Zhenan Sui",
    "Wei Sun"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In \\cite{Sui2019}, we proved the existence of a complete Lipschitz continuous weak admissible hypersurface with prescribed Weingarten curvature and asymptotic boundary at infinity in hyperbolic space under certain assumptions. In this paper, we investigate further on the existence of smooth solutions by establishing Pogorelov type interior second order estimates in hyperbolic space for some special asymptotic boundaries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-20T04:04:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic plateau problem",
      "hyperbolic space",
      "smooth solutions",
      "continuous weak admissible hypersurface",
      "lipschitz continuous weak admissible"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}