VOLUME-PRESERVING PL-MAPS BETWEEN POLYHEDRA

Abstract. We prove that for every two convex polytopes P, Q ∈ R d with vol(P) = vol(Q), there exists a continuous piecewise-linear (PL) volume-preserving map f: P → Q. The result extends to general PL-manifolds. The proof is inexplicit and uses the corresponding fact in the smooth category, proved by Moser in [Mo]. We conclude with various examples and combinatorial applications