{
  "id": "2203.10915",
  "version": "v1",
  "published": "2022-03-21T12:11:24.000Z",
  "updated": "2022-03-21T12:11:24.000Z",
  "title": "A Euclidean Fourier-analytic approach to vertical projections in the Heisenberg group",
  "authors": [
    "Terence L. J. Harris"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CA",
    "math.MG"
  ],
  "abstract": "An improved a.e. lower bound is given for Hausdorff dimension under vertical projections in the first Heisenberg group, with respect to the Carnot-Carath\\'eodory metric. This improves the known lower bound for sets $A$ with $1< \\dim A < 7/2$, and answers a question of F\\\"assler and Hovila. The approach uses the Euclidean Fourier transform.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-21T12:11:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A78",
      "28A80"
    ],
    "keywords": [
      "euclidean fourier-analytic approach",
      "vertical projections",
      "lower bound",
      "first heisenberg group",
      "euclidean fourier transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}