Cone-volume measures of polytopes
Metric Geometry
2013-11-28 v2 Differential Geometry
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.
Keywords
Cite
@article{arxiv.1305.5335,
title = {Cone-volume measures of polytopes},
author = {Martin Henk and Eva Linke},
journal= {arXiv preprint arXiv:1305.5335},
year = {2013}
}
Comments
Slightly revised version thanks to the suggestions of the referees and other readers; two figures added