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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

Geometric function theory. --- Mathematics. --- Math --- Science --- Function theory, Geometric --- Functions of complex variables

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Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings. Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem.

Geometric function theory. --- Functions of complex variables. --- Complex variables --- Elliptic functions --- Functions of real variables --- Function theory, Geometric --- Functions of complex variables

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The papers contained in this book address problems in one and several complex variables. The main theme is the extension of geometric function theory methods and theorems to several complex variables. The papers present various results on the growth of mappings in various classes as well as observations about the boundary behavior of mappings, via developing and using some semi group methods.

Geometric function theory --- Functions of several complex variables --- Fonctions, Théorie géométrique des --- Fonctions de plusieurs variables complexes --- Function theory, Geometric --- Functions of complex variables --- Fonctions, Theorie geometrique des

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This book discusses in detail the extension of the Schwarz-Pick inequality to higher order derivatives of analytic functions with given images. It is the first systematic account of the main results in this area. Recent results in geometric function theory presented here include the attractive steps on coefficient problems from Bieberbach to de Branges, applications of some hyperbolic characteristics of domains via Beardon-Pommerenke's theorem, a new interpretation of coefficient estimates as certain properties of the Poincaré metric, and a successful combination of the classical ideas of Littlewood, Löwner and Teichmüller with modern approaches. The material is complemented with historical remarks on the Schwarz Lemma and a chapter introducing some challenging open problems. The book will be of interest for researchers and postgraduate students in function theory and hyperbolic geometry.

Geometric function theory. --- Holomorphic functions. --- Ungleichung -- Funktionentheorie. --- Geometric function theory --- Holomorphic functions --- Applied Mathematics --- Calculus --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Functions, Holomorphic --- Function theory, Geometric --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Functions of several complex variables --- Functions of complex variables --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Geometry, Algebraic

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Fluid dynamics. --- Geometric function theory. --- Function theory, Geometric --- Functions of complex variables --- Dynamics --- Fluid mechanics --- Dinàmica de fluids --- Teoria geomètrica de funcions --- Funcions de variables complexes --- Aplicació conforme --- Aplicacions quasiconformes --- Diferencials quadràtiques --- Funcions univalents --- Mecànica de fluids --- Aerodinàmica --- Capa límit --- Equacions de Navier-Stokes --- Fluídica --- Fluïdització --- Hidrodinàmica --- Magnetohidrodinàmica --- Ones de xoc --- Turbulència --- Vòrtexs --- Tixotropia