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Courtade's conjecture on volumes of Minkowski sums with the ball

Courtade conjectured that for convex bodies B,C⊂RnB,C\subset\mathbb R^n, (∣B∣∣C∣)1/n+(∣B2n∣∣B2n+B+C∣)1/n≤∣B2n+B∣1/n∣B2n+C∣1/n. (|B||C|)^{1/n} + (|B_2^n||B_2^n+B+C|)^{1/n} \le |B_2^n+B|^{1/n}|B_2^n+C|^{1/n}. The paper proves that this inequality is false in every dimension n≥3n\ge3. In dimension 33, it gives an explicit geometric counterexample using two orthogonal double bodies of revolution. It then strengthens this by constructing zonoid counterexamples in every dimension n≥3n\ge3, including a six-generator zonotope in dimension 33 and smooth perturbative constructions in higher dimensions.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Aug 13, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-assisted. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Courtade's conjecture on volumes of Minkowski sums with the ball · Courtade’s conjecture

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Shouda Wang
human · human collaborator

Artem Zvavitch
human · human collaborator

Cheikh Saliou Ndiaye
human · human collaborator

GPT-5.6 Sol
model · ai model contributor · OpenAI

Matthieu Fradelizi
human · human collaborator

Alfredo Hubard
human · human collaborator

Auttawich Manui
human · human collaborator

Lineage and corrections

This event attributed to Shouda Wang

This event attributed to Artem Zvavitch

This event attributed to Cheikh Saliou Ndiaye

Courtade's conjecture on volumes of Minkowski sums with the ball parent of this event

Courtade conjectured that for convex bodies B,C⊂RnB,C\subset\mathbb R^n, (∣B∣∣C∣)1/n+(∣B2n∣∣B2n+B+C∣)1/n≤∣B2n+B∣1/n∣B2n+C∣1/n. (|B||C|)^{1/n} + (|B_2^n||B_2^n+B+C|)^{1/n} \le |B_2^n+B|^{1/n}|B_2^n+C|^{1/n}. The paper proves that this inequality is false in every dimension n≥3n\ge3. In dimension 33, it gives an explicit geometric counterexample using two orthogonal double bodies of revolution. It then strengthens this by constructing zonoid counterexamples in every dimension n≥3n\ge3, including a six-generator zonotope in dimension 33 and smooth perturbative constructions in higher dimensions. parent of this event

VibeMathed record: Courtade's conjecture on volumes of Minkowski sums with the ball evidence for this event

Courtade's conjecture on volumes of Minkowski sums with the ball evidence for this event

This event attributed to GPT-5.6 Sol

This event attributed to Matthieu Fradelizi

This event attributed to Alfredo Hubard

This event attributed to Auttawich Manui

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