{
  "abstract": "The Petty conjecture asserts that the quotient \\(V_n(ΠK)/V_n(K)^{n-1}\\) is minimized among all convex bodies precisely by ellipsoids. In this paper, we prove the conjecture for all convex bodies of revolution in \\(\\mathbb R^n\\), \\(n\\geq3\\), including the equality cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13517",
  "author_total": 1,
  "authors": [
    {
      "name": "Florian Mielke-Sulz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5r91ghna3d1p1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13517",
  "fulltext_url": null,
  "id": "5r91ghna3d1p1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13517",
  "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.MG"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7213329967",
  "pdf_url": "https://arxiv.org/pdf/2609.13517",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5r91ghna3d1p1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13517",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13517"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Petty Conjecture for Convex Bodies of Revolution",
  "title_text": "The Petty Conjecture for Convex Bodies of Revolution",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/5r91ghna3d1p1",
  "venue": "arXiv",
  "versions": []
}