{
  "id": "2107.13387",
  "version": "v2",
  "published": "2021-07-28T14:27:08.000Z",
  "updated": "2022-04-28T08:08:30.000Z",
  "title": "Curvature estimates for $p$-convex hypersurfaces of prescribed curvature",
  "authors": [
    "Weisong Dong"
  ],
  "comment": "15pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper, we establish the curvature estimates for $p$-convex hypersurfaces in $\\mathbb{R}^{n+1}$ of prescribed curvature with $p\\geq \\frac{n}{2}$. The existence of a star-shaped hypersurface of prescribed curvature is obtained. We also prove a type of interior $C^2$ estimates for solutions to the Dirichlet problem of the corresponding equation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-04-28T08:08:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "prescribed curvature",
      "curvature estimates",
      "convex hypersurfaces",
      "dirichlet problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}