{
  "id": "2008.06815",
  "version": "v1",
  "published": "2020-08-16T00:49:08.000Z",
  "updated": "2020-08-16T00:49:08.000Z",
  "title": "A Bernstein Type Theorem for Minimal Graphs over Convex Cones",
  "authors": [
    "Nick Edelen",
    "Zhehui Wang"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "Given any $n \\geq 2$, we show that if $\\Omega \\subsetneq \\mathbb{R}^n$ is an open, convex cone (e.g. a half-space), and $u : \\Omega \\to \\mathbb{R}$ is a solution to the minimal surface equation which agrees with a linear function on $\\partial\\Omega$, then $u$ must itself be linear.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-16T00:49:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bernstein type theorem",
      "convex cone",
      "minimal graphs",
      "minimal surface equation",
      "linear function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}