{
  "id": "1712.02242",
  "version": "v1",
  "published": "2017-12-06T15:48:08.000Z",
  "updated": "2017-12-06T15:48:08.000Z",
  "title": "Rank-one theorem and subgraphs of BV functions in Carnot groups",
  "authors": [
    "Sebastiano Don",
    "Annalisa Massaccesi",
    "Davide Vittone"
  ],
  "categories": [
    "math.AP",
    "math.FA",
    "math.MG"
  ],
  "abstract": "We prove a rank-one theorem \\`a la G. Alberti for the derivatives of vector-valued maps with bounded variation in a class of Carnot groups that includes Heisenberg groups $\\mathbb H^n$ for $n\\geq 2$. The main tools are properties relating the horizontal derivatives of a real-valued function with bounded variation and its subgraph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-06T15:48:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q15",
      "28A75",
      "49Q20"
    ],
    "keywords": [
      "carnot groups",
      "rank-one theorem",
      "bv functions",
      "bounded variation",
      "horizontal derivatives"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}