{
  "abstract": "We prove that many curved Kakeya problems, originally motivated by Hörmander's oscillatory integral problem, lift to the classical Kakeya problem in higher dimensions. As a consequence, if the classical Kakeya set conjecture were true in all dimensions, the families of curves whose curved Kakeya sets have full dimension are dense among Hörmander-type families. This is in contrast to the nowhere dense Bourgain's condition, which is a necessary condition for best-case curved Kakeya maximal function estimates. Furthermore the linear Kakeya set conjecture would imply a fairly complete understanding of Kakeya sets of quadratic curves, as first studied systematically by Wisewell. These results give a better understanding of a question posed by Guo--Guth--Nadjimzadah--Shen--Zhang, and they more generally show that the classical Kakeya conjecture in high dimensions rests on a broad range of curved Kakeya problems in lower dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06299",
  "author_total": 1,
  "authors": [
    {
      "name": "Arian Nadjimzadah"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2x5pg6qcgtn27.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06299",
  "fulltext_url": null,
  "id": "2x5pg6qcgtn27",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06299",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7212068932",
  "pdf_url": "https://arxiv.org/pdf/2609.06299",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2x5pg6qcgtn27.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2609.06299",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06299"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Lifting curved Kakeya sets to linear Kakeya sets",
  "title_text": "Lifting curved Kakeya sets to linear Kakeya sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/2x5pg6qcgtn27",
  "venue": "arXiv",
  "versions": []
}