{
  "abstract": "A universal cover in is a measurable set that contains a congruent copy of any set of diameter 1. Lebesgue's universal covering problem, posed in 1914, asks for the convex set of smallest area that serves as a universal cover in the plane (). A simple universal cover in is provided by the classical theorem of Jung, which states that any set of diameter 1 in an ‐dimensional Euclidean space is contained in a ball of radius ; in other words, is a universal cover in . We show that in high dimensions, Jung's ball is asymptotically optimal with respect to the volume, namely, for any universal cover ,",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2512.04023",
  "author_total": 4,
  "authors": [
    {
      "name": "A. Arman"
    },
    {
      "name": "A. Bondarenko"
    },
    {
      "name": "A. Prymak"
    },
    {
      "name": "Danylo Radchenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1y5cjfan1zf50.bib",
  "cited_by": 0,
  "doi": "10.1112/blms.70514",
  "fulltext_url": null,
  "id": "1y5cjfan1zf50",
  "issns": [
    "0024-6093",
    "1469-2120"
  ],
  "landing_url": "https://hal.science/hal-05851837v1",
  "language": "en",
  "licence": "CC-BY-NC",
  "licence_label": "CC BY-NC",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-mg"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W4417034898",
  "pdf_url": "https://onlinelibrary.wiley.com/doi/pdfdirect/10.1112/blms.70514",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": "London Mathematical Society",
  "ris": "https://research.draconitic.com/paper/1y5cjfan1zf50.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:20:13Z",
      "native_id": "hal-05851837",
      "source": "hal",
      "url": "https://hal.science/hal-05851837v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-mg",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On asymptotic Lebesgue's universal covering problem",
  "title_text": "On asymptotic Lebesgue's universal covering problem",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T12:20:44Z",
  "url": "https://research.draconitic.com/paper/1y5cjfan1zf50",
  "venue": "Bulletin of the London Mathematical Society",
  "versions": []
}