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The logarithmic Brunn-Minkowski conjecture for origin-symmetric convex bodies

Theorem 1.1: for every n≥1n\ge1, origin-symmetric convex bodies K,LK,L and 0≤λ≤10\le\lambda\le1, ∣W[hK1−λhLλ]∣≥∣K∣1−λ∣L∣λ|W[h_K^{1-\lambda}h_L^\lambda]|\ge|K|^{1-\lambda}|L|^\lambda. Corollary 1.2 gives the symmetric LpL_p Brunn-Minkowski inequality for full-dimensional origin-symmetric bodies and every 0<p<10<p<1, via the monotone implication recorded by Boroczky-Lutwak-Yang-Zhang. The proof reduces to a variance bound for sums of even powers of linear forms, proved in moment-measure coordinates. It does not treat equality cases, non-symmetric bodies (where the inequality is false in general), or the uniqueness question for the even logarithmic Minkowski problem.

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Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. 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: The logarithmic Brunn-Minkowski conjecture for origin-symmetric convex bodies · Log-Brunn-Minkowski conjecture

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Registry verification: lean checked · announcement · candidate

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VibeMathed
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Unreleased internal OpenAI model
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Lean proof (OAI.LogBrunnMinkowski.main)

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Comparator statement: LogBrunnMinkowski.lean

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This event attributed to Unreleased internal OpenAI model

Comparator statement: LogBrunnMinkowski.lean evidence for this event

VibeMathed record: The logarithmic Brunn-Minkowski conjecture for origin-symmetric convex bodies evidence for this event

Boroczky-Lutwak-Yang-Zhang, The log-Brunn-Minkowski inequality (2012) evidence for this event

The logarithmic Brunn-Minkowski conjecture for origin-symmetric convex bodies evidence for this event

Lean proof (OAI.LogBrunnMinkowski.main) evidence for this event

Theorem 1.1: for every n≥1n\ge1, origin-symmetric convex bodies K,LK,L and 0≤λ≤10\le\lambda\le1, ∣W[hK1−λhLλ]∣≥∣K∣1−λ∣L∣λ|W[h_K^{1-\lambda}h_L^\lambda]|\ge|K|^{1-\lambda}|L|^\lambda. Corollary 1.2 gives the symmetric LpL_p Brunn-Minkowski inequality for full-dimensional origin-symmetric bodies and every 0<p<10<p<1, via the monotone implication recorded by Boroczky-Lutwak-Yang-Zhang. The proof reduces to a variance bound for sums of even powers of linear forms, proved in moment-measure coordinates. It does not treat equality cases, non-symmetric bodies (where the inequality is false in general), or the uniqueness question for the even logarithmic Minkowski problem. parent of this event

The logarithmic Brunn-Minkowski conjecture for origin-symmetric convex bodies parent of this event

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The logarithmic Brunn-Minkowski conjecture for origin-symmetric convex bodies — Mathematical Frontier Network