The log-Brunn-Minkowski inequality in ℝ³

Yang, Yunlong; Zhang, Deyan

doi:10.1090/proc/14366

The log-Brunn-Minkowski inequality in $\mathbb {R}^3$
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by Yunlong Yang and Deyan Zhang

Proc. Amer. Math. Soc. 147 (2019), 4465-4475

DOI: https://doi.org/10.1090/proc/14366

Published electronically: June 27, 2019

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Abstract:

Böröczky, Lutwak, Yang, and Zhang have recently proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane which is stronger than the classical Brunn-Minkowski inequality. This paper establishes the log-Brunn-Minkowski, log-Minkowski, $L_p$-Minkowski, and $L_p$-Brunn-Minkowski inequalities for two classes of convex bodies in $\mathbb {R}^3$.

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