{
  "abstract": "We prove the Falconer-type bound $\\dim_{\\mathrm H}F\\geq u+1$ for planar circular $(u,v)$-Furstenberg sets whenever $0<u\\leq1$, $0<v\\leq3$, and $2u+v\\geq3$. The same bound holds for smooth cinematic curve families. This resolves the circular Furstenberg conjecture of Green, Harris, Ou, Ren, and Tammen in its full Falconer range $2u+v\\geq3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35213",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiang Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/385p21wp0z5gp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35213",
  "fulltext_url": null,
  "id": "385p21wp0z5gp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35213",
  "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"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7223850728",
  "pdf_url": "https://arxiv.org/pdf/2610.35213",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/385p21wp0z5gp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35213",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35213"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Falconer estimate for circular and cinematic Furstenberg problem",
  "title_text": "Falconer estimate for circular and cinematic Furstenberg problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/385p21wp0z5gp",
  "venue": "arXiv",
  "versions": []
}