Logarithmic and L_(p) Brunn–Minkowski inequalities and the B-conjecture
OpenAI research collection · 1 manuscript · Source checked 2026-10-19
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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< p< 1.
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MANUSCRIPT 01
The logarithmic Brunn–Minkowski conjecture
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< p< 1. Combined with Saroglou's transfer theorem and a support-subspace reduction, it yields the logarithmic inequality for every…
Full source abstract
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< p< 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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