On extensions of the Loomis-Whitney inequality and Ball's inequality for concave, homogeneous measures

摘要

The Loomis-Whitney inequality states that the volume of a convex body is bounded by the product of volumes of its projections onto orthogonal hyperplanes. We provide an extension of both this fact and a generalization of this fact due to Ball to the context of q-concave, 1/q-homogeneous measures. (C) 2020 Elsevier Inc. All rights reserved.