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Edited By Reiner Kuhnau, Martin Luther Universität, Halle-Wittenberg, Germany
Description 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.
Audience
Institutes of mathematics (and computer sciences). Institutes of physics and engineering.
Contents 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 Teichmuller 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.
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