{
  "id": "1809.04586",
  "version": "v1",
  "published": "2018-09-12T17:50:26.000Z",
  "updated": "2018-09-12T17:50:26.000Z",
  "title": "The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group",
  "authors": [
    "Sebastiano Nicolussi",
    "Francesco Serra Cassano"
  ],
  "comment": "29 pages, 2 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "We prove that, in the first Heisenberg group $\\mathbb{H}$, an entire locally Lipschitz intrinsic graph admitting vanishing first variation of its sub-Riemannian area and non-negative second variation must be an intrinsic plane, i.e., a coset of a two dimensional subgroup of $\\mathbb{H}$. Moreover two examples are given for stressing result's sharpness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-12T17:50:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C17",
      "49Q20"
    ],
    "keywords": [
      "heisenberg group",
      "bernstein problem",
      "locally lipschitz intrinsic graph",
      "graph admitting vanishing first",
      "lipschitz intrinsic graph admitting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}