GL(n) equivariant Minkowski valuations

TL;DR

This paper classifies all continuous Minkowski valuations that are equivariant under the general linear group GL(n), completing the broader understanding of such valuations in convex geometry.

Contribution

It provides a complete classification of all continuous GL(n) equivariant Minkowski valuations, advancing the theoretical framework in convex geometric analysis.

Findings

Complete classification of continuous GL(n) equivariant Minkowski valuations

Integration of recent results to finalize the description of all such valuations

Enhancement of the theoretical understanding of Minkowski valuations in convex geometry

Abstract

A classification of all continuous GL(n) equivariant Minkowski valuations on convex bodies in $\mathbb{R}^n$ is established. Together with recent results of F.E. Schuster and the author, this article therefore completes the description of all continuous GL(n) intertwining Minkowski valuations.