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

TL;DR

This paper applies Kotrbaty's recent theorem on valuations to derive new inequalities for mixed volumes of convex bodies, bridging valuation theory and geometric inequalities.

Contribution

It introduces novel inequalities for mixed volumes by leveraging Kotrbaty's theorem, connecting valuation theory with convex geometry.

Findings

Derived new inequalities for mixed volumes

Connected valuation theory with geometric inequalities

Extended the application of Kotrbaty's theorem

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.