{
  "id": "0801.3741",
  "version": "v2",
  "published": "2008-01-24T13:48:52.000Z",
  "updated": "2016-02-15T12:02:11.000Z",
  "title": "Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane",
  "authors": [
    "Luigi Ambrosio",
    "Bruce Kleiner",
    "Enrico Le Donne"
  ],
  "comment": "29 pages, final version",
  "journal": "J. Geom. Anal. 19 (2009), no. 3, 509-540",
  "categories": [
    "math.AP",
    "math.DG",
    "math.GR",
    "math.MG"
  ],
  "abstract": "We consider sets of locally finite perimeter in Carnot groups. We show that if E is a set of locally finite perimeter in a Carnot group G, then for almost every x in G with respect to the perimeter measure of E, some tangent of E at x is a vertical halfspace. This is a partial extension of a theorem of Franchi-Serapioni-Serra Cassano in step 2 Carnot groups: they have shown that, for almost every x, E has a unique tangent at x, and this tangent is a vertical halfspace.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-24T13:48:52.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-02-15T12:02:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A75",
      "49Q15",
      "58C35"
    ],
    "keywords": [
      "carnot group",
      "tangent hyperplane",
      "locally finite perimeter",
      "rectifiability",
      "vertical halfspace"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}