Cone-volume measures of polytopes

doi:10.1016/j.aim.2013.11.015

Advances in Mathematics

Volume 253, 1 March 2014, Pages 50-62

In memory of Fiona Prohaska

https://doi.org/10.1016/j.aim.2013.11.015 Get rights and content

Under an Elsevier user license

open archive

Abstract

The cone-volume measure of a polytope with centroid at the origin is proved to satisfy the subspace concentration condition. As a consequence a conjectured (a dozen years ago) fundamental sharp affine isoperimetric inequality for the U-functional is completely established – along with its equality conditions.

MSC

52A40

52B11

Keywords

Cone-volume measure

Subspace concentration condition

U-functional

Centro-affine inequalities

Log-Minkowski problem

Centroid

Polytope

Cited by (0)

¹: Supported by Deutsche Forschungsgemeinschaft; He 2272/5-1.