Harmonic mappings in the plane

Peter Duren
Cambridge University Press
 9780521641210
0-521-64121-7

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,.

read more…

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.