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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

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The logarithmic Brunn–Minkowski conjecture

Sep 23, 2026·paper.pdfLean

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.

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

Manuscripts in this family · 1

The logarithmic Brunn–Minkowski conjecture

Logarithmic and L $_{p}$ Brunn–Minkowski inequalities and the B-conjecture