On the regularity of the composition of diffeomorphisms

Abstract

For M M a closed manifold or the Euclidean space R n \mathbb {R}^n we present a detailed proof of regularity properties of the composition of H s H^s -regular diffeomorphisms of M M for s > 1 2 dim ⁡ M + 1 s > \frac {1}{2}\dim M+1 .