{
  "id": "1509.06675",
  "version": "v1",
  "published": "2015-09-22T16:35:49.000Z",
  "updated": "2015-09-22T16:35:49.000Z",
  "title": "On the distance sets of AD-regular sets",
  "authors": [
    "Tuomas Orponen"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CA",
    "math.MG"
  ],
  "abstract": "I prove that if $K \\subset \\mathbb{R}^{2}$ is $s$-Ahlfors-David regular with $s \\geq 1$, then $$\\overline{\\dim}_{\\mathrm{B}} D(K) = 1,$$ where $D(K) = \\{|x - y| : x,y \\in K\\}$ is the distance set of $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-22T16:35:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distance set",
      "ad-regular sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150906675O"
    }
  }
}