Quasiconformal Mappings in the Plane [Paperback]

I. Geometric Definition of a Quasiconformal Mapping.- to Chapter I.- ? 1. Topological Properties of Plane Sets.- ? 2. Conformal Mappings of Plane Domains.- ? 3. Definition of a Quasiconformal Mapping.- ? 4. Conformal Module and Extremal Length.- ? 5. Two Basic Properties of Quasiconformal Mappings.- ? 6. Module of a Ring Domain.- ? 7. Characterization of Quasiconformality with the Help of Ring Domains.- ? 8. Extension Theorems for Quasiconformal Mappings.- ? 9. Local Characterization of Quasiconformality.- II. Distortion Theorems for Quasiconformal Mappings.- to Chapter II.- ?1. Ring Domains with Extremal Module.- ? 2. Module of Gr?tzschs Extremal Domain.- ? 3. Distortion under a Bounded Quasiconformal Mapping of a Disc.- ? 4. Order of Continuity of Quasiconformal Mappings.- ? 5. Convergence Theorems for Quasiconformal Mappings.- ? 6. Boundary Values of a Quasiconformal Mapping.- ? 7. Quasisymmetric Functions.- ? 8. Quasiconformal Continuation.- ? 9. Circular Dilatation.- III. Auxiliary Results from Real Analysis.- to Chapter III.- ? 1. Measure and Integral.- ? 2. Absolute Continuity.- ? 3. Differentiability of Mappings of Plane Domains.- ? 4. Module of a Family of Arcs or Curves.- ? 5. Approximation of Measurable Functions.- ? 6. Functions with Lp-derivatives.- ? 7. Hubert Transformation.- IV. Analytic Characterization of a Quasiconformal Mapping.- to Chapter IV.- ? 1. Analytic Properties of a Quasiconformal Mapping.- ? 2. Analytic Definition of Quasiconformality.- ? 3. Variants of the Geometric Definition.- ? 4. Characterization of Quasiconformality with the Help of the Circular Dilatation.- ? 5. Complex Dilatationl.- V. Quasiconformal Mappings with Prescribed Complex Dilatation.- to Chapter V.- ? l. Existence Theorem.- ? 2. Local Dilatation Measures.- ? 3. Removable Point Sets.- ? 4. Approximation of a Quasiconformal Mapping.- ? 5. Application of the Hilbert Transformation to Quasiconformal Mappings21l.- ? 6. Conformality at a Point.- ? 7. Regularity of a Mappinlc1