Log-Brunn-Minkowski inequality under symmetry

Böröczky, Károly; Kalantzopoulos, Pavlos

doi:10.1090/tran/8691

Log-Brunn-Minkowski inequality under symmetry
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by Károly J. Böröczky and Pavlos Kalantzopoulos PDF

Trans. Amer. Math. Soc. 375 (2022), 5987-6013 Request permission

Abstract:

We prove the log-Brunn-Minkowski conjecture for convex bodies with symmetries to $n$ independent hyperplanes, and discuss the equality case and the uniqueness of the solution of the related case of the logarithmic Minkowski problem. We also clarify a small gap in the known argument classifying the equality case of the log-Brunn-Minkowski conjecture for unconditional convex bodies.

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