Handbook of Complex Analysis

Reiner Kuhnau (Edited by)

9780444828453, Elsevier Science

Hardback, published 5 December 2002

548 pages
24.1 x 16.5 x 3.2 cm, 1.14 kg

"A thoroughly written author index as well as a subject index simplifies the research for the reader. A well-written book". --Rudolf Rupp - Zeitschrift Fuer Angewandte Mathematik Und Mechanik, 2005.

Geometric Function Theory is a central part of Complex Analysis (one complex variable). The Handbook of Complex Analysis - Geometric Function Theory deals with this field and its many ramifications and relations to other areas of mathematics and physics. The theory of conformal and quasiconformal mappings plays a central role in this Handbook, for example a priori-estimates for these mappings which arise from solving extremal problems, and constructive methods are considered. As a new field the theory of circle packings which goes back to P. Koebe is included. The Handbook should be useful for experts as well as for mathematicians working in other areas, as well as for physicists and engineers.

Preface.
List of Contributors.
Univalent and multivalent functions (W.K. Hayman).
Conformal maps at the boundary (Ch. Pommerenke).
Extremal quasiconformal mapings of the disk (E. Reich).
Conformal welding (D.H. Hamilton).
Siegel disks and geometric function theory in the work of Yoccoz (D.H. Hamilton).
Sufficient confidents for univalence and quasiconformal extendibility of analytic functions (L.A. Aksent'ev, P.L. Shabalin).
Bounded univalent functions (D.V. Prokhorov).
The *-function in complex analysis (A. Baernstein II).
Logarithmic geometry, exponentiation, and coefficient bounds in the theory of univalent functions and nonoverlapping domains (A.Z. Grinshpan).
Circle packing and discrete analytic function theory (K. Stephenson).
Extreme points and support points (T.H. MacGregory, D.R. Wilken).
The method of the extremal metric (J.A. Jenkins).
Universal Teichmüller space (F.P. Gardiner, W.J. Harvey).
Application of conformal and quasiconformal mappings and their properties in approximation theory (V.V. Andrievskii).
Author Index.
Subject Index.

Subject Areas: Geometry [PBM], Functional analysis & transforms [PBKF], Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB]