Crofton measures and Minkowski valuations

TL;DR

This paper characterizes continuous Minkowski valuations compatible with rigid motions and establishes a Brunn-Minkowski inequality for their intrinsic volumes, advancing geometric measure theory.

Contribution

It provides a new description of such valuations and introduces a related Brunn-Minkowski inequality, linking valuations with classical geometric inequalities.

Findings

Characterization of continuous rigid motion compatible Minkowski valuations

A new Brunn-Minkowski type inequality for intrinsic volumes of these valuations

Enhanced understanding of geometric inequalities in valuation theory

Abstract

A description of continuous rigid motion compatible Minkowski valuations is established. As an application, we present a Brunn-Minkowski type inequality for intrinsic volumes of these valuations.