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
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.