{
  "id": "2106.11937",
  "version": "v1",
  "published": "2021-06-22T17:19:58.000Z",
  "updated": "2021-06-22T17:19:58.000Z",
  "title": "On the Dimension of Kakeya Sets in the First Heisenberg Group",
  "authors": [
    "Jiayin Liu"
  ],
  "comment": "11 pages, 3 figures",
  "categories": [
    "math.CA",
    "math.MG"
  ],
  "abstract": "We define Kakeya sets in the Heisenberg group and show that the Heisenberg Hausdorff dimension of Kakeya sets in the first Heisenberg group is at least 3. This lower bound is sharp since, under our definition, the $\\{xoy\\}$-plane is a Kakeya set with Heisenberg Hausdorff dimension 3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-22T17:19:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A75",
      "28A78",
      "28A80"
    ],
    "keywords": [
      "first heisenberg group",
      "heisenberg hausdorff dimension",
      "define kakeya sets",
      "lower bound",
      "definition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}