{
  "id": "1306.6355",
  "version": "v1",
  "published": "2013-06-26T20:34:37.000Z",
  "updated": "2013-06-26T20:34:37.000Z",
  "title": "The Lusin theorem and horizontal graphs in the Heisenberg group",
  "authors": [
    "Piotr Hajlasz",
    "Jacob Mirra"
  ],
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "In this paper we prove that every collection of measurable functions $f_\\alpha$, $|\\alpha|=m$ coincides a.e. with $m$th order derivatives of a function $g\\in C^{m-1}$ whose derivatives of order $m-1$ may have any modulus of continuity weaker than that of a Lipschitz function. This is a stronger version of earlier results of Lusin, Moonens-Pfeffer and Francos. As an application we construct surfaces in the Heisenberg group with tangent spaces being horizontal a.e.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-26T20:34:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "46E30"
    ],
    "keywords": [
      "heisenberg group",
      "horizontal graphs",
      "lusin theorem",
      "th order derivatives",
      "tangent spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.6355H"
    }
  }
}