The dual Loomis–Whitney inequality

Abstract

We establish a dual version of the Loomis–Whitney inequality for isotropic measures with complete equality conditions, where the sharp lower bound is given in terms of the volumes of hyperplane sections. For the special case of cross measures, we can drop the condition that the underlying body has centroid at the origin, yielding an independent proof of a result of Meyer's [‘A volume inequality concerning sections of convex sets’, Bull. London Math. Soc. 20 (1988) 151–155].