Kotrbaty's theorem on valuations and geometric inequalities for convex bodies
Metric Geometry
2020-10-20 v3
Abstract
Very recently J. Kotrbaty has proven general inequalities for translation invariant smooth valuations formally analogous to the Hodge- Riemann bilinear relations in the Kahler geometry. The goal of this note is to apply Kotrbaty's theorem to obtain a few apparently new inequalities for mixed volumes of convex bodies.
Cite
@article{arxiv.2010.01859,
title = {Kotrbaty's theorem on valuations and geometric inequalities for convex bodies},
author = {Semyon Alesker},
journal= {arXiv preprint arXiv:2010.01859},
year = {2020}
}
Comments
18 pages; discussion of some of the equality cases is added; minor corrections