Logarithmic and L_{p} Brunn–Minkowski inequalities and the B-conjecture

Proves the logarithmic Brunn–Minkowski inequality for origin-symmetric convex bodies in every dimension, and the scalar-dilation B-conjecture for all even log-concave Radon measures. For Lebesgue volume it also proves the additive L_p Brunn–Minkowski inequality for full-dimensional origin-symmetric convex bodies throughout 0\lt p\lt 1. (Lean)

Manuscript

The logarithmic Brunn–Minkowski conjecture

September 23, 2026 · source · Lean formalization available · cite as \cite{OAI:The-logarithmic-Brunn-Minkowski-conjecture-September-23-2026}

We prove the logarithmic Brunn–Minkowski conjecture for arbitrary origin-symmetric convex bodies in every dimension. The theorem also gives the symmetric L_p Brunn–Minkowski inequality for every 0\lt p\lt 1. Combined with Saroglou's transfer theorem and a support-subspace reduction, it yields the logarithmic inequality for every even log-concave Radon measure and the scalar-dilation (B)-conjecture.

Result 091 · Convex and metric geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.