Conformal Geometry and Quasiregular Mappings

  • Authors
  • Matti Vuorinen

Part of the Lecture Notes in Mathematics book series (LNM, volume 1319)

Table of contents

  1. Front Matter
    Pages I-XIX
  2. Matti Vuorinen
    Pages 1-47
  3. Matti Vuorinen
    Pages 48-119
  4. Matti Vuorinen
    Pages 120-172
  5. Matti Vuorinen
    Pages 173-192
  6. Back Matter
    Pages 193-209

About this book

Introduction

This book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory. The text leads the reader to the frontier of current research and covers some most recent developments in the subject, previously scatterd through the literature. A major role in this monograph is played by certain conformal invariants which are solutions of extremal problems related to extremal lengths of curve families. These invariants are then applied to prove sharp distortion theorems for quasiregular mappings. One of these extremal problems of conformal geometry generalizes a classical two-dimensional problem of O. Teichmüller. The novel feature of the exposition is the way in which conformal invariants are applied and the sharp results obtained should be of considerable interest even in the two-dimensional particular case. This book combines the features of a textbook and of a research monograph: it is the first introduction to the subject available in English, contains nearly a hundred exercises, a survey of the subject as well as an extensive bibliography and, finally, a list of open problems.

Keywords

DEX Invariant Sharp behavior boundary element method development extrema form function geometry mapping theorem time

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0077904
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-19342-5
  • Online ISBN 978-3-540-39207-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book