Geometric Function Theory and Non-linear Analysis

by Tadeusz Iwaniec, Gaven Martin

Overview

A survey of recent developments in the field of non-linear analysis and the geometry of mappings. Sobolev mappings, quasiconformal mappings, or deformations, between subsets of Euclidean space, or manifolds or more general geometric objects may arise as the solutions to certain optimization problems in the calculus of variations or in non-linear elasticity, as the solutions to differential equations (particularly in conformal geometry), as local co-ordinates on a manifold or as geometric realizations of abstract isomorphisms between spaces such as those that arise in dynamical systems (for instance in holomorphic dynamics and Kleinian groups). In each case the regularity and geometric properties of these mappings and related non-linear quantities such as Jacobians, tells something about the problems and the spaces under consideration.

Product Details

ISBN-13:	9780198509295
Publisher:	Oxford University Press
Publication date:	12/13/2001
Series:	Oxford Mathematical Monographs
Edition description:	New Edition
Pages:	568
Product dimensions:	9.30(w) x 6.36(h) x 1.33(d)

Table of Contents

1. Introduction and overview2. Conformal mappings3. Stability of the Möbius group4. Sobolev theory and function spaces5. The Liouville theorem6. Mappings of finite distortion7. Continuity8. Compactness9. Topics from Multilinear Algebra10. Differential Forms11. Beltrami equations12. Riesz transforms13. Integral estimates14. The Gehrng lemma15. The governing equations16. Topological properties of mappings of bounded distortion17. Painlevé's theorem in space18. Even dimensions19. Picard and Montel theorems in space20. Conformal structures21. Uniformly quasiregular mappings22. Quasiconformal groups23. Analytic continuation for Beltrami systemsBibliographyIndex

Editorial Reviews

"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

From the Publisher