{
  "id": "2105.08890",
  "version": "v1",
  "published": "2021-05-19T02:34:16.000Z",
  "updated": "2021-05-19T02:34:16.000Z",
  "title": "Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group",
  "authors": [
    "Robert Young"
  ],
  "comment": "30 pages, 5 figures",
  "categories": [
    "math.CA",
    "math.MG"
  ],
  "abstract": "In this paper, we give a necessary and sufficient condition for a graphical strip in the Heisenberg group $\\mathbb{H}$ to be area-minimizing in the slab $\\{-1<x<1\\}$. We show that our condition is necessary by introducing a family of deformations of graphical strips based on varying a vertical curve. We show that it is sufficient by showing that strips satisfying the condition have monotone epigraphs. We use this condition to show that any area-minimizing ruled entire intrinsic graph in the Heisenberg group is a vertical plane and to find a boundary curve that admits uncountably many fillings by area-minimizing surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-19T02:34:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q05",
      "53C17",
      "49Q20"
    ],
    "keywords": [
      "heisenberg group",
      "area-minimizing ruled graphs",
      "bernstein problem",
      "graphical strip",
      "area-minimizing ruled entire intrinsic graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}