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. · A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane)
Author(s): Reiner Kuhnau
Edition: 1
Publisher: Elsevier Science & Technology
Year: 2002
Language: English
Pages: 547
Cover......Page 1
Preface......Page 6
List of Contributors......Page 10
Table of Contents......Page 12
1. Univalent and multivalent functions......Page 14
2. Conformal maps at the boundary......Page 50
3. Extremal quasiconformal mappings of the disk......Page 88
4. Conformal welding......Page 150
5. Area distortion of quasiconformal mappings......Page 160
6. Siegel disks and geometric function theory in the work of Yoccoz......Page 174
7. Sufficient conditions for univalence and quasiconformal extendibility of analytic functions......Page 181
8. Bounded univalent functions......Page 219
9. The *-function in complex analysis......Page 241
10. Logarithmic geometry, exponentiation, and coefficient bounds in the theory of univalent functions and nonoverlapping domains......Page 284
11. Circle packing and discrete analytic function theory......Page 344
12. Extreme points and support points......Page 382
13. The method of the extremal metric......Page 404
14. Universal Teichmtiller space......Page 468
15. Application of conformal and quasiconformal mappings and their properties in approximation theory......Page 504
Author Index......Page 532
Subject Index......Page 542
