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Complex analysis --- Geometric function theory --- Congresses. --- 51 --- -Function theory, Geometric --- Functions of complex variables --- Mathematics --- Congresses --- -Mathematics --- 51 Mathematics --- -51 Mathematics --- Function theory, Geometric --- Geometric function theory - Congresses.
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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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The book contains papers published in a Special Issue of Axioms, entitled "New Developments in Geometric Function Theory". An Editorial describes the 14 papers devoted to the study of complex-valued functions which present new outcomes related to special classes of univalent and bi-univalent functions, new operators and special functions associated with differential subordination and superordination theories, fractional calculus, and certain applications in geometric function theory.
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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.
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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.
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Aims at giving a presentation of ideas that arise from the problems of planar fluid dynamics and which are interesting from the point of view of geometric function theory and potential theory. This book is concerned with geometric problems for Hele-Shaw flows.
Fluid dynamics. --- Geometric function theory. --- Function theory, Geometric --- Functions of complex variables --- Dynamics --- Fluid mechanics --- Differential equations, partial. --- Potential theory (Mathematics). --- Partial Differential Equations. --- Potential Theory. --- Classical and Continuum Physics. --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Partial differential equations --- Partial differential equations. --- Continuum physics. --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics
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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
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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
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Geometric function theory. --- Functions of complex variables. --- Geometry, Differential. --- Retracts, Theory of. --- Hermitian operators. --- Fonctions, Théorie géométrique des. --- Fonctions d'une variable complexe. --- Géométrie différentielle. --- Rétractes, Théorie des. --- Opérateurs hermitiens. --- Théorie géométrique des fonctions --- Fonctions d'une variable complexe --- Géométrie différentielle --- Théorie des rétractes --- Opérateurs hermitiens --- Geometric function theory --- Functions of complex variables --- Geometry, Differential --- Retracts, Theory of --- Hermitian operators --- Operators, Hermitian --- Operators, Symmetrical --- Symmetrical operators --- Linear operators --- Topology --- Differential geometry --- Complex variables --- Elliptic functions --- Functions of real variables --- Function theory, Geometric
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