{
  "abstract": "We show that an almost-everywhere upper bound $b\\geq 1$ for the Hausdorff dimension of visible parts of all compact planar sets implies the upper bound $d-2+b$ for visible parts of all compact sets $K$ in $\\mathbb{R}^d$, $d\\geq3$. Inserting the sharp planar bound $b=3/2$ of Orponen and Rutar \\cite{OrponenRutar2026} gives $\\dim_H \\mathrm{Vis}_e(K)\\leq d-1/2$ for almost every $e\\in S^{d-1}$. This would answer their Question 1.9 sharply in all dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35388",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuming He"
    },
    {
      "name": "Changbiao Jian"
    },
    {
      "name": "Yudong Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/85vcgq2sxc3cm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35388",
  "fulltext_url": null,
  "id": "85vcgq2sxc3cm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35388",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7214763257",
  "pdf_url": "https://arxiv.org/pdf/2609.35388",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/85vcgq2sxc3cm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35388",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35388"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Visibility problem in higher dimensions",
  "title_text": "Visibility problem in higher dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/85vcgq2sxc3cm",
  "venue": "arXiv",
  "versions": []
}