# MathSciDoc: An Archive for Mathematician ∫

#### Convex and Discrete Geometry mathscidoc:1703.40034

For $1 \leq p < \infty$, Ludwig, Haberl and Parapatits classified $L_p$ Minkowski valuations intertwining the special linear group with additional conditions such as homogeneity and continuity. In this paper,a complete classification of $L_p$ Minkowski valuations intertwining the special linear group on polytopes without any additional conditions is established for $p \geq 1$ including $p = \infty$. For $n=3$ and $p=1$, there exist valuations not mentioned before.
$L_\infty$ Minkowski valuation, $L_\infty$ projection body, $L_p$ Minkowski valuation, function-valued valuation, $\sln$ contravariant, $\sln$ covariant
@inproceedings{jin2016lp,
title={Lp MINKOWSKI VALUATIONS ON POLYTOPES},
author={Jin Li, and Gangsong Leng},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170310021513378225650},