Handbook of Complex Analysis
Elsevier, Dec 5, 2002 - Mathematics - 548 pages
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)
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Chapter 3 Extremal quasiconformal mappings of the disk
Chapter 4 Conformal welding
Chapter 5 Area distortion of quasiconformal mappings
Chapter 6 Siegel disks and geometric function theory in the work of Yoccoz
Chapter 7 Sufficient conditions for univalence and quasiconformal extendibility of analytic functions
Chapter 8 Bounded univalent functions
Chapter 9 The function in complex analysis
Chapter 11 Circle packing and discrete analytic function theory
Chapter 12 Extreme points and support points
Chapter 13 The method of the extremal metric
Chapter 14 Universal Teichmüller space
Chapter 15 Application of conformal and quasiconformal mappings and their properties in approximation theory
Chapter 10 Logarithmic geometry exponentiation and coefficient bounds in the theory of univalent functions and nonoverlapping domains
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Abbildung Acad Ahlfors Amer analytic functions Bieberbach conjecture boundary point boundary values Branges Chapter circle packing coefficients of univalent complex dilatation Complex Variables conformal mapping conformal welding connected domains constant convex defined denote discrete dx dy English transl equation example exists extremal metric extremal problems extremal quasiconformal mappings finite function f(z geometric function theory Grötzsch Grunsky harmonic measure holomorphic homeomorphism hyperbolic I.M. Milin inequality integral J.A. Jenkins Jordan curve Koebe function Kühnau Lemma Let f logarithmic London Math Löwner mapping f meromorphic functions method Möbius transformation module norm obtained plane polynomials Pommerenke Proc proof properties proved quadratic differential quasiconformal extension quasiconformal mappings quasisymmetric result Riemann surface Russian satisfies schlicht Section sequence simply connected Strebel subharmonic sufficient conditions support points symmetrization Teichmüller mapping Teichmüller space trajectories uniquely extremal unit disk Univ univalent functions zero
Page 34 - Functions which map the interior of the unit circle upon simple regions, Ann.