{
  "abstract": "We prove the existence of a sharp threshold $p_0 \\approx 26.265\\ldots$, such that for every $n\\in\\mathbb{N}$ and $p\\geq p_0$, the volume maximizing section of the unit ball of $\\ell_p^n$ is the section with Ball's hyperplane $(\\frac{e_1+e_2}{\\sqrt{2}})^\\perp$, whereas for $p\\in(2,p_0)$ the asymptotic maximizer as the ambient dimension $n\\to\\infty$ is the hyperplane orthogonal to the diagonal vector $\\frac{e_1+\\cdots+e_n}{\\sqrt{n}}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07619",
  "author_total": 2,
  "authors": [
    {
      "name": "Silouanos Brazitikos"
    },
    {
      "name": "Alexandros Eskenazis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c1pt5txmg01va.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07619",
  "fulltext_url": null,
  "id": "c1pt5txmg01va",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07619",
  "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.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07619",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c1pt5txmg01va.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07619",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07619"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The dimension-free threshold for maximal sections of $\\ell_p$",
  "title_text": "The dimension-free threshold for maximal sections of ℓ_p",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/c1pt5txmg01va",
  "venue": "arXiv",
  "versions": []
}