The log-Brunn-Minkowski inequality in ${\mathbb{R}}^3$

Abstract

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

arXiv comment11 pages, 2 figures

References in corpus (2)

• The Logarithmic Minkowski Problem
• Ehrhart polynomial and Successive Minima

Cited by in corpus (1)

• On the $L_p$ Brunn-Minkowski theory and the $L_p$ Minkowski problem for $C$-coconvex sets