{
  "id": "2407.11475",
  "version": "v1",
  "published": "2024-07-16T08:14:20.000Z",
  "updated": "2024-07-16T08:14:20.000Z",
  "title": "Subsets of vertical planes in the first Heisenberg group",
  "authors": [
    "Terence L. J. Harris"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CA",
    "math.MG"
  ],
  "abstract": "It is shown that if $A$ is a Borel subset of the first Heisenberg group contained in some vertical subgroup, then vertical projections almost surely do not decrease the Hausdorff dimension of $A$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-16T08:14:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A78",
      "28A80"
    ],
    "keywords": [
      "first heisenberg group",
      "vertical planes",
      "borel subset",
      "hausdorff dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}