Lp Minkowski valuations on polytopes

Abstract For 1 ≤ p ∞ , 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 ≥ 1 including p = ∞ . For n = 3 and p = 1 , there exist valuations not mentioned before.