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Moduli of Families of Curves for Conformal and Quasiconformal Mappings

  • Book
  • © 2002

Overview

Authors:
  1. Alexander Vasil’ev
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1788)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-IX
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  2. 1. Introduction

    • Alexander Vasil’ev
    Pages 1-5

  3. 2. Moduli of Families of Curves and Extremal Partitions

    • Alexander Vasil’ev
    Pages 7-55

  4. 3. Moduli in Extremal Problems for Conformal Mapping

    • Alexander Vasil’ev
    Pages 57-139

  5. 4. Moduli in Extremal Problems for Quasiconformal Mapping

    • Alexander Vasil’ev
    Pages 141-174

  6. 5. Moduli on Teichmüller Spaces

    • Alexander Vasil’ev
    Pages 175-196

  7. References

    • Alexander Vasil’ev
    Pages 197-206

  8. List of symbols and Index

    • Alexander Vasil’ev
    Pages 207-211

  9. Back Matter

    Pages 213-215
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Keywords

About this book

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.

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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