{
  "abstract": "Godbersen's long-standing conjecture states that the mixed volumes of any convex body $K \\subset \\mathbb R^n$ satisfy $V(K[k], -K[n-k])\\le \\binom{n}{k} \\operatorname{vol}(K)$ for any $k \\in \\{1, \\dots, n - 1\\}$, with equality if and only if $K$ is an $n$-simplex. Kotrbatý and Mouamine recently proved the inequality in full generality, and showed that if $K$ is a (full-dimensional) polytope attaining equality, it must be a simplex. We complete the characterization of the equality case: if $K \\subset \\mathbb R^n$ is a convex body for which $V(K[k], -K[n-k]) = \\binom{n}{k} \\operatorname{vol}(K)$ for some $k \\in \\{1, \\dots, n -1\\}$, then $K$ is an $n$-simplex. By a similar method, we characterize the equality case in the higher-order Godbersen inequality conjectured by Schneider and by Kotrbatý.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04527",
  "author_total": 3,
  "authors": [
    {
      "name": "Omer Friedland"
    },
    {
      "name": "Eli Putterman"
    },
    {
      "name": "Maud Szusterman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ekjx4m3n1r8b4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04527",
  "fulltext_url": null,
  "id": "ekjx4m3n1r8b4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04527",
  "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",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7220706784",
  "pdf_url": "https://arxiv.org/pdf/2610.04527",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ekjx4m3n1r8b4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.04527",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04527"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The equality case in Godbersen's inequality and its generalizations",
  "title_text": "The equality case in Godbersen's inequality and its generalizations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/ekjx4m3n1r8b4",
  "venue": "arXiv",
  "versions": []
}