On the regularity of the composition of diffeomorphisms

TL;DR

This paper provides a detailed proof of the regularity properties of composing $H^s$-regular diffeomorphisms on closed manifolds or Euclidean space, for sufficiently large $s$, contributing to the understanding of their smoothness behavior.

Contribution

It offers a rigorous and detailed proof of the regularity of composition of $H^s$-diffeomorphisms, clarifying conditions for smoothness in geometric analysis.

Findings

Composition preserves $H^s$-regularity under specified conditions

Provides explicit regularity estimates for composed diffeomorphisms

Enhances understanding of the structure of diffeomorphism groups

Abstract

For $M$ being a closed manifold or the Euclidean space we present a detailed proof of regularity properties of the composition of $H^s$-regular diffeomorphisms of $M$ for $s > 1/2\dim M + 1$.