Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics

The book presents a research area in geometric function theory concerned with harmonic quasiconformal mappings and hyperbolic type metrics defined on planar and multidimensional domains. The classes of quasiconformal and quasiregular mappings are well established areas of study in this field as these classes are natural and fruitful generalizations of the class of analytic functions in the planar case. The book contains many concrete examples, as well as detailed proofs and explanations of motivations behind given results, gradually bringing the reader to the forefront of current research in the area. This monograph was written for a wide readership from graduate students of mathematical analysis to researchers working in this or related areas of mathematics who want to learn the tools or work on open problems listed in various parts of the book.

Covers harmonic quasiconformal mappings and hyperbolic type metrics in the plane and in the space Includes an extensive bibliography of the field Self contained presentation of a currently active research area in Geometric Function

Inhalt
Introduction.- Quasiconformal and quasiregular harmonic mappings.- Hyperbolic type metrics.- Distance Ratio Metric.- Bi-Lipschitz property of HQC mappings.- Quasi-nearly subharmonic functions and QC mappings.- Possible research directions.