Cone-volume measure of general centered convex bodies

摘要

We show that the cone-volume measure of a convex body with centroid at the origin satisfies the subspace concentration condition. This extends former results obtained in the discrete as well as in the symmetric case and implies, among others, a conjectured best possible inequality for the U-functional of a convex body. (C) 2015 Elsevier Inc. All rights reserved.