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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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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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The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups theory, iteration theory and related topics. Written by experts in geometric function theory in one and several complex variables, it focuses on new research frontiers in this area and on challenging open problems. The book is intended for graduate students and researchers working in complex analysis, several complex variables and geometric function theory.
Geometric function theory. --- Mathematics. --- Dynamics. --- Ergodic theory. --- Functional analysis. --- Functions of complex variables. --- Several Complex Variables and Analytic Spaces. --- Functions of a Complex Variable. --- Functional Analysis. --- Dynamical Systems and Ergodic Theory. --- Complex variables --- Elliptic functions --- Functions of real variables --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Math --- Science --- Function theory, Geometric --- Functions of complex variables --- Differential equations, partial. --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Partial differential equations
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