Univalent Functions and Teichmller Spaces [Paperback]

I Quasiconformal Mappings.- to Chapter I.- 1. Conformal Invariants.- 1.1 Hyperbolic metric.- 1.2 Module of a quadrilateral.- 1.3 Length-area method.- 1.4 Rengels inequality.- 1.5 Module of a ring domain.- 1.6 Module of a path family.- 2. Geometric Definition of Quasiconformal Mappings.- 2.1 Definitions of quasiconformality.- 2.2 Normal families of quasiconformal mappings.- 2.3 Compactness of quasiconformal mappings.- 2.4 A distortion function.- 2.5 Circular distortion.- 3. Analytic Definition of Quasiconformal Mappings.- 3.1 Dilatation quotient.- 3.2 Quasiconformal diffeomorphisms.- 3.3 Absolute continuity and differentiability.- 3.4 Generalized derivatives.- 3.5 Analytic characterization of quasiconformality.- 4. Beltrami Differential Equation.- 4.1 Complex dilatation.- 4.2 Quasiconformal mappings and the Beltrami equation.- 4.3 Singular integrals.- 4.4 Representation of quasiconformal mappings.- 4.5 Existence theorem.- 4.6 Convergence of complex dilatations.- 4.7 Decomposition of quasiconformal mappings.- 5. The Boundary Value Problem.- 5.1 Boundary function of a quasiconformal mapping.- 5.2 Quasisymmetric functions.- 5.3 Solution of the boundary value problem.- 5.4 Composition of Beurling-Ahlfors extensions.- 5.5 Quasi-isometry.- 5.6 Smoothness of solutions.- 5.7 Extremal solutions.- 6. Quasidiscs.- 6.1 Quasicircles.- 6.2 Quasiconformal reflections.- 6.3 Uniform domains.- 6.4 Linear local connectivity.- 6.5 Arc condition.- 6.6 Conjugate quadrilaterals.- 6.7 Characterizations of quasidiscs.- II Univalent Functions.- to Chapter II.- 1. Schwarzian Derivative.- 1.1 Definition and transformation rules.- 1.2 Existence and uniqueness.- 1.3 Norm of the Schwarzian derivative.- 1.4 Convergence of Schwarzian derivatives.- 1.5 Area theorem.- 1.6 Conformal mappings of a disc.- 2. Distance between Simply Connected Domains.- 2.1 Distance from a disc.- 2.2 Distance function and coefficient problems.- 2.3 Boundary rotation.- 2.4 Domains of bounded boundary rotation.- 2.5 Upper els›