An Introduction to the Theory of Higher-Dimensional Quasiconformal Mappings
About this Title
Frederick W. Gehring, Gaven J. Martin, Massey University, Auckland, New Zealand and Bruce P. Palka, National Science Foundation, Arlington, VA
Publication: Mathematical Surveys and Monographs
Publication Year: 2017; Volume 216
ISBNs: 978-0-8218-4360-4 (print); 978-1-4704-4046-6 (online)
MathSciNet review: MR3642872
MSC: Primary 30-02; Secondary 30C62, 30C65
This book offers a modern, up-to-date introduction to quasiconformal mappings from an explicitly geometric perspective, emphasizing both the extensive developments in mapping theory during the past few decades and the remarkable applications of geometric function theory to other fields, including dynamical systems, Kleinian groups, geometric topology, differential geometry, and geometric group theory. It is a careful and detailed introduction to the higher-dimensional theory of quasiconformal mappings from the geometric viewpoint, based primarily on the technique of the conformal modulus of a curve family. Notably, the final chapter describes the application of quasiconformal mapping theory to Mostow's celebrated rigidity theorem in its original context with all the necessary background.
This book will be suitable as a textbook for graduate students and researchers interested in beginning to work on mapping theory problems or learning the basics of the geometric approach to quasiconformal mappings. Only a basic background in multidimensional real analysis is assumed.
Graduate students and researchers interested in mapping theory.
Table of Contents
- Topology and analysis
- Conformal mappings in Euclidean space
- The moduli of curve families
- Rings and condensers
- Quasiconformal mappings
- Mapping problems
- The Tukia-Väisälä extension theorem
- The Mostow rigidity theorem and discrete Möbius groups