Curvature functionals on convex bodies
Metric Geometry
2022-04-19 v1 Differential Geometry
Abstract
We investigate the weighted affine surface areas which appear in the recently established Steiner formula of the Brunn Minkowski theory. We show that they are valuations on the set of convex bodies and prove isoperimetric inequalities for them. We show that they are related to divergences of the cone measures of the convex body and its polar, namely the Kullback-Leibler divergence and the R\'enyi-divergence.
Cite
@article{arxiv.2204.07611,
title = {Curvature functionals on convex bodies},
author = {Kateryna Tatarko and Elisabeth M. Werner},
journal= {arXiv preprint arXiv:2204.07611},
year = {2022}
}