Moduli of Families of Curves for Conformal and Quasiconformal Mappings

Alexander Vasil’ev (auth.)3540438467, 9783540438465

The monograph is concerned with the modulus of families of curves on Riemann surfaces and its applications to extremal problems for conformal, quasiconformal mappings, and the extension of the modulus onto Teichmüller spaces. The main part of the monograph deals with extremal problems for compact classes of univalent conformal and quasiconformal mappings. Many of them are grouped around two-point distortion theorems. Montel’s functions and functions with fixed angular derivatives are also considered. The last portion of problems is directed to the extension of the modulus varying the complex structure of the underlying Riemann surface that sheds some new light on the metric problems of Teichmüller spaces.

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Table of contents :
1. Introduction….Pages 1-5
2. Moduli of Families of Curves and Extremal Partitions….Pages 7-55
3. Moduli in Extremal Problems for Conformal Mapping….Pages 57-139
4. Moduli in Extremal Problems for Quasiconformal Mapping….Pages 141-174
5. Moduli on Teichmüller Spaces….Pages 175-196
References….Pages 197-206
List of symbols and Index….Pages 207-211