{
  "id": "2408.09428",
  "version": "v1",
  "published": "2024-08-18T10:02:02.000Z",
  "updated": "2024-08-18T10:02:02.000Z",
  "title": "Curvature estimates for semi-convex solutions of asymptotic Plateau problem in $\\mathbb{H}^{n+1}$",
  "authors": [
    "Han Hong",
    "Ruijia Zhang"
  ],
  "comment": "38 pages, comments welcome",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we consider the asymptotic $\\sigma_k$ Plateau problem in hyperbolic space. We establish $C^2$ estimates for semi-convex complete hypersurfaces satisfying constant $\\sigma_k$ curvature with a prescribed asymptotic boundary at the infinity for $2\\leq k\\leq n-2$ . The result is based on a new crucial concavity inequality derived for hessian equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-18T10:02:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "35J60",
      "53C40"
    ],
    "keywords": [
      "asymptotic plateau problem",
      "curvature estimates",
      "semi-convex solutions",
      "semi-convex complete hypersurfaces satisfying constant",
      "crucial concavity inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}