Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 091-01. The logarithmic Brunn–Minkowski conjecture
Manuscript map · lines 4255–4264
OpenAI@2026-10-07#rem:oai-p-091-01
Authors: OpenAI. Family 091.
Title: The logarithmic Brunn–Minkowski conjecture.
Abstract: We prove the logarithmic Brunn–Minkowski conjecture for arbitrary origin-symmetric convex bodies in every dimension. The theorem also gives the symmetric Lp 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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