Kotrbaty's theorem on valuations and geometric inequalities for convex bodies

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.

arXiv comment18 pages; discussion of some of the equality cases is added; minor corrections