{
  "id": "2408.03919",
  "version": "v1",
  "published": "2024-08-07T17:22:54.000Z",
  "updated": "2024-08-07T17:22:54.000Z",
  "title": "Favard length and quantitative rectifiability",
  "authors": [
    "Damian Dąbrowski"
  ],
  "comment": "89 pages",
  "categories": [
    "math.CA",
    "math.MG"
  ],
  "abstract": "The Favard length of a Borel set $E\\subset\\mathbb{R}^2$ is the average length of its orthogonal projections. We prove that if $E$ is Ahlfors 1-regular and it has large Favard length, then it contains a big piece of a Lipschitz graph. This gives a quantitative version of the Besicovitch projection theorem. As a corollary, we answer questions of David and Semmes and of Peres and Solomyak. We also make progress on Vitushkin's conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-07T17:22:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A75",
      "28A78"
    ],
    "keywords": [
      "quantitative rectifiability",
      "besicovitch projection theorem",
      "large favard length",
      "answer questions",
      "average length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 89,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}