{
  "id": "2208.03597",
  "version": "v1",
  "published": "2022-08-06T23:50:55.000Z",
  "updated": "2022-08-06T23:50:55.000Z",
  "title": "Exceptional set estimates for orthogonal and radial projections in $\\mathbb{R}^n$",
  "authors": [
    "Paige Dote",
    "Shengwen Gan"
  ],
  "comment": "25 pages, 2 figures",
  "categories": [
    "math.CA",
    "math.MG"
  ],
  "abstract": "We give different proofs of classic Falconer-type and Kaufman-type exceptional estimates for orthogonal projections using the high-low method. With the new techniques, we resolve Liu's conjecture on radial projections: given a Borel set $A\\subset \\mathbb{R}^n$, we have \\[ \\text{dim} (\\{x\\in \\mathbb{R}^n \\setminus A \\mid \\text{dim}(\\pi_x(A))<\\text{dim} A\\}) \\leq \\lceil \\text{dim} A\\rceil. \\]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-06T23:50:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exceptional set estimates",
      "radial projections",
      "resolve lius conjecture",
      "kaufman-type exceptional estimates",
      "classic falconer-type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}