Harmonic Mappings in the Plane


Harmonic Mappings in the Plane

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.


 Reviews:

'This book is devoted to the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces.' Monatshefte für Mathematik

'For all students in this filed Duren's book will be essential reading. it will also be the classic reference book in this area.' Proceedings of the Edinburgh Mathematical Society

'Those who are sensible to the beauty of complex functions and Riemann surfaces will certainly enjoy reading this nicely written … book.' Mathematical Geology

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