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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Bibliographic Information

Book Title: Moduli of Families of Curves for Conformal and Quasiconformal Mappings
Authors: Alexander Vasil’ev
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/b83857
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2002
Softcover ISBN: 978-3-540-43846-5Published: 23 July 2002
eBook ISBN: 978-3-540-45437-3Published: 19 October 2004
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: IX, 214
Topics: Functions of a Complex Variable

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Table of contents (7 chapters)

Front Matter

1. Introduction

2. Moduli of Families of Curves and Extremal Partitions

3. Moduli in Extremal Problems for Conformal Mapping

4. Moduli in Extremal Problems for Quasiconformal Mapping

5. Moduli on Teichmüller Spaces

References

List of symbols and Index

Back Matter

About this book