{
  "id": "1205.3010",
  "version": "v1",
  "published": "2012-05-14T13:09:49.000Z",
  "updated": "2012-05-14T13:09:49.000Z",
  "title": "Transversality of isotropic projections, unrectifiability and Heisenberg groups",
  "authors": [
    "Risto Hovila"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We show that the family of $m$-dimensional isotropic projections in $\\R^{2n}$ is transversal. As an application we show that the Besicovitch-Federer projection theorem holds for isotropic projections. We also use transversality to obtain almost sure estimates on the Hausdorff dimension of isotropic projections of subsets $E \\subset \\R^{2n}$. These results may also be applied to gain information on the horizontal projections of the Heisenberg group $\\H^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-14T13:09:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "28A78",
      "53D05"
    ],
    "keywords": [
      "heisenberg group",
      "transversality",
      "unrectifiability",
      "besicovitch-federer projection theorem holds",
      "dimensional isotropic projections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.3010H"
    }
  }
}