{
  "abstract": "We study the $(n-2)$-plane Kakeya problem in $\\mathbb{R}^n$ ($n\\geq4$) subject to convex Wolff axioms. In other words, we study finite families of $δ$-neighborhoods of $(n-2)$-plane segments ($δ$-flakes) in $\\mathbb{R}^n$, with the property that not too many of them can be contained inside a common convex set. Our main result is that the union of $δ$-flakes from such a set must have almost maximal volume. This can be viewed as a higher-dimensional generalization of Wang and Zahl's work for $δ$-tubes in $\\mathbb{R}^3$. The latter implies the Kakeya set conjecture in $\\mathbb{R}^3$. As a consequence, we resolve Rogers' $2$-plane Kakeya problem in $\\mathbb{R}^4$ subject to certain curvature conditions on two-dimensional families of direction subspaces in the Grassmannian $\\mathrm{Gr}(4,2)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10603",
  "author_total": 4,
  "authors": [
    {
      "name": "Chun-Kit Lai"
    },
    {
      "name": "Yixuan Pang"
    },
    {
      "name": "Rahul Sethi"
    },
    {
      "name": "Chenjian Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3cpht5z5qzfvb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10603",
  "fulltext_url": null,
  "id": "3cpht5z5qzfvb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10603",
  "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",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7221084810",
  "pdf_url": "https://arxiv.org/pdf/2610.10603",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3cpht5z5qzfvb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10603",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10603"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Kakeya problem for codimension-two planes in $\\mathbb{R}^n$",
  "title_text": "The Kakeya problem for codimension-two planes in ℝ^n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/3cpht5z5qzfvb",
  "venue": "arXiv",
  "versions": []
}