{
  "abstract": "We prove that the mixed volume of a convex body of fixed positive volume with its reflection about the origin is maximized by simplices. This confirms a conjecture of C. Godbersen from 1938 and refines the classical Rogers-Shephard inequality. We also prove that simplices are the only extremizers among convex polytopes. Finally, we use this inequality to prove an $L_p$-version of the Rogers-Shephard inequality for convex bodies containing the origin and show that, for any $p\\in(1,\\infty]$, the only extremizers are simplices with a vertex at the origin.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.20387",
  "author_total": 2,
  "authors": [
    {
      "name": "Jan Kotrbatý"
    },
    {
      "name": "Mohamed A. Mouamine"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5kqeymr49b3pt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.20387",
  "fulltext_url": null,
  "id": "5kqeymr49b3pt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.20387",
  "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": "W7170154721",
  "pdf_url": "https://arxiv.org/pdf/2607.20387",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5kqeymr49b3pt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2607.20387",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.20387"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Godbersen's conjecture and the $L_p$-Rogers-Shephard inequality",
  "title_text": "Godbersen's conjecture and the L_p-Rogers-Shephard inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/5kqeymr49b3pt",
  "venue": "arXiv",
  "versions": []
}