{
  "id": "2004.08275",
  "version": "v1",
  "published": "2020-04-17T14:41:53.000Z",
  "updated": "2020-04-17T14:41:53.000Z",
  "title": "The Bernstein problem for elliptic Weingarten multigraphs",
  "authors": [
    "Isabel Fernandez",
    "Jose A. Galvez",
    "Pablo Mira"
  ],
  "comment": "24 pages, 7 figures",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We prove that any complete, uniformly elliptic Weingarten surface in Euclidean $3$-space whose Gauss map image omits an open hemisphere is a cylinder or a plane. This generalizes a classical theorem by Hoffman, Osserman and Schoen for constant mean curvature surfaces. In particular, this proves that planes are the only complete, uniformly elliptic Weingarten multigraphs. We also show that this result holds for a large class of non-uniformly elliptic Weingarten equations. In particular, this solves in the affirmative the Bernstein problem for entire graphs for that class of elliptic equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-17T14:41:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "53C42",
      "35J15",
      "35J60"
    ],
    "keywords": [
      "bernstein problem",
      "gauss map image omits",
      "constant mean curvature surfaces",
      "non-uniformly elliptic weingarten equations",
      "uniformly elliptic weingarten surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}