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)
Institutes of mathematics (and computer sciences). Institutes of physics and engineering.
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.
- No. of pages:
- © North Holland 2002
- 5th December 2002
- North Holland
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"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.