The purpose of this book is to present a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. The modulus method was initiated by Arne Beurling and Lars Ahlfors to study conformal mappings, and later this method was extended and enhanced by several others. The techniques are geometric and they have turned out to be an indispensable tool in the study of quasiconformal and quasiregular mappings as well as their generalizations. The book is based on recent research papers and extends the modulus method beyond the classical applications of the modulus techniques presented in many monographs.

Zusammenfassung

Based on recent research papers, this book presents a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. It contains an extensive bibliography.

Inhalt
and Notation.- Moduli and Capacity.- Moduli and Domains.- Q-Homeomorphisms with Q? Lloc1.- Q-homeomorphisms with Q in BMO.- More General Q-Homeomorphisms.- Ring Q-Homeomorphisms.- Mappings with Finite Length Distortion (FLD).- Lower Q-Homeomorphisms.- Mappings with Finite Area Distortion.- On Ring Solutions of the Beltrami Equation.- Homeomorphisms with Finite Mean Dilatations.- On Mapping Theory in Metric Spaces.