Harmonic Mappings In The Plane - Peter L. Duren
Camridge University Press (2004)
In Collection

Read It:
Harmonic Maps, Harmonic Maps, Mathematics / Differential Equations, Mathematics / General, Mathematics / Probability & Statistics / General

Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. 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. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It is designed to introduce non-specialists to a beautiful area of complex analysis and geometry.

Product Details
LoC Classification QA614.73 .D87 2004
Dewey 514.74
No. of Pages 236
Height x Width 240 x 158 mm