{
  "abstract": "For $0<d\\leq1/4$, let $\\mathcal{C}(d)$ be the four-corner Cantor set with Hausdorff dimension $s_d=\\log 4/\\log(1/d)$. Peres, Simon, and Solomyak, as well as Mattila, asked for which $d$ the measure $\\Hau^{s_d}(p_θ(\\mathcal{C}(d)))$ is positive for almost every direction $θ$. It was open for the range $1/9\\leq d\\leq1/6$. In this paper, we show that, for $δ< d\\leq1/6$, there is a set $\\IP(d)$ of positive Lebesgue measure such that for almost every $θ\\in\\IP(d)$, $\\Hau^{s_d}(p_θ(\\mathcal{C}(d)))=0$, where $δ=0.155124983896014\\ldots$ is the unique zero in $(1/9,1/6)$ of the polynomial $P(d)=1-7d+3d^2+4d^3-2d^4-d^5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04684",
  "author_total": 1,
  "authors": [
    {
      "name": "Chong-Wei Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4n6rrjwbe0kd2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04684",
  "fulltext_url": null,
  "id": "4n6rrjwbe0kd2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04684",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7211865548",
  "pdf_url": "https://arxiv.org/pdf/2609.04684",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4n6rrjwbe0kd2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04684",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04684"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "On the Hausdorff measure of projections of self-similar sets",
  "title_text": "On the Hausdorff measure of projections of self-similar sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/4n6rrjwbe0kd2",
  "venue": "arXiv",
  "versions": []
}