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 Teichmuller 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 Teichmuller spaces.
- ISBN10 3540454373
- ISBN13 9783540454373
- Publish Date 1 September 2006 (first published 23 July 2002)
- Publish Status Active
- Publish Country US
- Imprint Springer
- Format eBook
- Language English