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On the regularity of the composition of diffeomorphisms


About this Title

H. Inci, Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Schwitzerland, T. Kappeler, Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Schwitzerland and P. Topalov, Department of Mathematics, Northeastern University, Boston, Massachusetts 02115

Publication: Memoirs of the American Mathematical Society
Publication Year 2013: Volume 226, Number 1062
ISBNs: 978-0-8218-8741-7 (print); 978-1-4704-1062-9 (online)
DOI: http://dx.doi.org/10.1090/S0065-9266-2013-00676-4
Published electronically: March 28, 2013
Keywords:Group of diffeomorphisms, regularity of composition, Euler equation
MSC (2010): Primary 58D17, 35Q31, 76N10

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Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. Groups of diffeomorphisms on $\mathbb {R}^n$
  • Chapter 3. Diffeomorphisms of a closed manifold
  • Chapter 4. Differentiable structure of $H^s(M, N)$
  • Appendix A.
  • Appendix B.

Abstract


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

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