Breakthrough Tracker record

A claimed proof of Godbersen's mixed-volume conjecture

The authors claim the sharp Godbersen bound for the mixed volume of a convex body and its reflection, confirming the conjectured simplex value. They also prove an Lp Rogers–Shephard inequality and classify the equality cases among convex polytopes.

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Stable ID: math-godbersen-conjecture-2026
Revision: math-godbersen-conjecture-2026.v2
Field: Mathematics · Convex geometry
Evidence: Tier 1 · Peer reviewed: No
Record state: Provisional · Preprint-only claimed proof; review pending
Last checked: 2026-10-02

AI role

No substantive AI role was disclosed in the inspected manuscript.

Record details

Problem or result: Godbersen's 1938 conjecture on mixed volumes of a convex body and its reflection
Authors: Jan Kotrbatý and Mohamed A. Mouamine
Institutions: Mathematical Institute of Charles University
Result date: Current v2 revised September 14, 2026

Why it matters

The conjecture has stood since 1938 and sits inside the Brunn–Minkowski theory of convex bodies and mixed volumes.

Limits

The current v2 remains unrefereed. It simplifies the main proof and adds a symmetric-body proposition, but no independent specialist assessment, journal acceptance or formal verification was located.

Sources

Primary: Kotrbatý and Mouamine, Godbersen's conjecture and the Lp-Rogers–Shephard inequality

Correction and revision history

2026-07-22 — Added as a version-one preprint claim pending independent specialist review.
2026-10-02 — Reviewed v2, which simplifies the main proof and adds a symmetric-body Lp Rogers–Shephard proposition; classification unchanged.

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