Geometric Function Theory and Non-linear Analysis [Hardcover]

1. Introduction and overview
2. Conformal mappings
3. Stability of the M?bius group
4. Sobolev theory and function spaces
5. The Liouville theorem
6. Mappings of finite distortion
7. Continuity
8. Compactness
9. Topics from Multilinear Algebra
10. Differential Forms
11. Beltrami equations
12. Riesz transforms
13. Integral estimates
14. The Gehrng lemma
15. The governing equations
16. Topological properties of mappings of bounded distortion
17. Painlev?'s theorem in space
18. Even dimensions
19. Picard and Montel theorems in space
20. Conformal structures
21. Uniformly quasiregular mappings
22. Quasiconformal groups
23. Analytic continuation for Beltrami systems
Bibliography
Index

Every reader interested in the modern viewpoint of geometric function theory will find a wide range of appealing topics in this book. It is particularly useful to see how some highly sohisticated machinery of real and harmonic analysis is developed and employed. This book will become a standard reference for the field. --Mathematical Reviews