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Moduli of Families of Curves for Conformal and Quasiconformal Mappings

  • Authors
  • Alexander Vasil’ev

Part of the Lecture Notes in Mathematics book series (LNM, volume 1788)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Alexander Vasil’ev
    Pages 1-5
  3. Alexander Vasil’ev
    Pages 57-139
  4. Alexander Vasil’ev
    Pages 175-196
  5. Alexander Vasil’ev
    Pages 197-206
  6. Alexander Vasil’ev
    Pages 207-211
  7. Back Matter
    Pages 213-215

About this book

Introduction

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.

Keywords

Modulus Riemann surface Riemann surfaces Teichmüller space conformal and quasiconformal mappings

Bibliographic information

  • DOI https://doi.org/10.1007/b83857
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-43846-5
  • Online ISBN 978-3-540-45437-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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