{
  "id": "2001.11304",
  "version": "v1",
  "published": "2020-01-30T13:28:55.000Z",
  "updated": "2020-01-30T13:28:55.000Z",
  "title": "An improved bound for the dimension of $(α,2α)$-Furstenberg sets",
  "authors": [
    "Kornélia Héra",
    "Pablo Shmerkin",
    "Alexia Yavicoli"
  ],
  "comment": "29 pages",
  "categories": [
    "math.CA",
    "math.CO",
    "math.MG"
  ],
  "abstract": "We show that given $\\alpha \\in (0, 1)$ there is a constant $c=c(\\alpha) > 0$ such that any planar $(\\alpha, 2\\alpha)$-Furstenberg set has Hausdorff dimension at least $2\\alpha + c$. This improves several previous bounds, in particular extending a result of Katz-Tao and Bourgain. We follow the Katz-Tao approach with suitable changes, along the way clarifying, simplifying and/or quantifying many of the steps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-30T13:28:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A78",
      "05B30"
    ],
    "keywords": [
      "furstenberg set",
      "hausdorff dimension",
      "katz-tao approach",
      "suitable changes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}