© 1988

Conformal Geometry and Quasiregular Mappings

  • Authors

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


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.


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

About the authors

Bibliographic information

  • Book Title Conformal Geometry and Quasiregular Mappings
  • Authors Matti Vuorinen
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lecture Notes in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-19342-5
  • eBook ISBN 978-3-540-39207-1
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages XXII, 214
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Potential Theory
    Differential Geometry
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