SL(n)-Covariant $L_p$-Minkowski Valuations

TL;DR

This paper classifies all continuous SL(n)-covariant $L_p$-Minkowski valuations on convex bodies, highlighting the $L_p$-moment body operators as key examples of such valuations.

Contribution

It provides a complete classification of these valuations, identifying the $L_p$-moment body operators as the fundamental prototypes.

Findings

All such valuations are classified explicitly.

$L_p$-moment body operators are the main examples.

The classification is complete and comprehensive.

Abstract

All continuous SL(n)-covariant $L_p$-Minkowski valuations defined on convex bodies are completely classified. The $L_p$-moment body operators turn out to be the nontrivial prototypes of such maps.