Synopses & Reviews
Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. It contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It introduces non-specialists to a beautiful area of complex analysis and geometry.
Synopsis
This first comprehensive account of the theory of planar harmonic mappings, meant for non-specialists, treats both the generalizations of univalent analytic functions and the connections with minimal surfaces. Included are background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation.
Synopsis
The theory of planar harmonic mappings straddles both complex analysis and differential geometry. Harmonic mappings are natural analogues of analytic univalent functions, but they also provide an essential tool for the study of minimal surfaces. They have been the object of intensive research by complex analysts in the last few years. This book is the first extensive exposition, treating both analytic and geometric aspects of harmonic mappings. This introduction is designed for graduate students and researchers in all areas of mathematics.
Synopsis
A comprehensive account, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces.