{
  "abstract": "We settle the long-standing Godbersen conjecture that the mixed volume of a convex body of fixed positive volume with its reflection about the origin is maximized precisely by simplices. For the proof, we establish a new characterization of simplices by a natural incidence relation on the face lattice. Moreover, we establish a higher-order generalization of the Godbersen inequality and show that simplices are the only nontrivial equality cases, confirming a conjecture of Schneider from 2000.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06806",
  "author_total": 4,
  "authors": [
    {
      "name": "Filip Fryš"
    },
    {
      "name": "Jan Kotrbatý"
    },
    {
      "name": "Mohamed A. Mouamine"
    },
    {
      "name": "Shouda Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cej641et7nddr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06806",
  "fulltext_url": null,
  "id": "cej641et7nddr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06806",
  "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.MG"
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      "openalex",
      "2604|Point processes and geometric inequalities"
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  ],
  "openalex": "W7220648380",
  "pdf_url": "https://arxiv.org/pdf/2610.06806",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cej641et7nddr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.06806",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06806"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Higher-order Godbersen inequality and a characterization of simplices via the face lattice",
  "title_text": "Higher-order Godbersen inequality and a characterization of simplices via the face lattice",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/cej641et7nddr",
  "venue": "arXiv",
  "versions": []
}