{
  "abstract": "Godbersen's long-standing conjecture states that the mixed volumes of any convex body $K \\subset \\R^n$ satisfy $V(K[k], -K[n-k])\\le \\binom{n}{k} \\vol(K)$ for any $k \\in \\{1, \\dots, n - 1\\}$, with equality if and only if $K$ is an $n$-simplex. Kotrbat\\'y 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, resolving Godbersen's conjecture in the affirmative: if $K \\subset \\R^n$ is a convex body for which $V(K[k], -K[n-k]) = \\binom{n}{k} \\vol(K)$ for some $k \\in \\{1, \\dots, n -1\\}$, then $K$ is an $n$-simplex.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Omer Friedland"
    },
    {
      "name": "Eli Putterman"
    },
    {
      "name": "Maud Szusterman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/80gnh3s5sbmf5.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "80gnh3s5sbmf5",
  "issns": [],
  "landing_url": "https://hal.science/hal-05776242v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-mg"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05776242/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/80gnh3s5sbmf5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:46Z",
      "native_id": "hal-05776242",
      "source": "hal",
      "url": "https://hal.science/hal-05776242v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-mg",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the equality case in the Kotrbatý-Mouamine inequality",
  "title_text": "On the equality case in the Kotrbatý-Mouamine inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:46Z",
  "url": "https://research.draconitic.com/paper/80gnh3s5sbmf5",
  "venue": "HAL",
  "versions": []
}