Lecture Notes in Mathematics

Vasil'ev, Alexander

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.

Details

Published by: Springer

Publication Date: 2002-07-23

Format: Paperback

ISBN-13: 9783540438465

DOI: 10.1007/b83857

Dimensions: 235cm x155cm

Pages: 214