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.v1- Field
- Mathematics · Convex geometry
- Evidence
- Tier 1 · Peer reviewed: No
- Record state
- Provisional · Preprint-only claimed proof; review pending
- Last checked
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
- Preprint submitted July 22, 2026
Why it matters
The conjecture has stood since 1938 and sits inside the Brunn–Minkowski theory of convex bodies and mixed volumes.
Limits
This is a same-day version-one preprint. No independent specialist assessment, journal acceptance or formal verification was located. The paper's uniqueness statement is for convex polytopes; it does not claim a full equality-case classification for every convex body.
Sources
Correction and revision history
- 2026-07-22 — Added as a version-one preprint claim pending independent specialist review.
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