Mosers theorem on manifolds with corners

Mosers theorem (1965) states that the diffeomorphism group of a compact manifold acts transitively on the space of all smooth positive densities with fixed volume. Here we describe the extension of this result to manifolds with corners. In particular we obtain Mosers theorem on simplices. The proof is based on Banyagas paper (1974), where Mosers theorem is proven for manifolds with boundary. A cohomological interpretation of Banyagas operator is given, which allows a proof of Lefschetz duality using differential forms.