Harmonic Mappings in the Plane

ISBN-13: 9780521641210 / Angielski / Twarda / 2004 / 226 str.

Peter Duren; Bela Bollobas; W. Fulton

Opis

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.

Recenzje

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

Spis treści

1. Preliminaries; 2. Local properties of harmonic mappings; 3. Harmonic mappings onto convex regions; 4. Harmonic self-mappings of the disk; 5. Harmonic univalent functions; 6. Extremal problems; 7. Mapping problems; 8. Additional topics; 9. Minimal surfaces; 10. Curvature of minimal surfaces; Appendix; References.