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Conformal Geometry and Quasiregular Mappings

  • Book
  • © 1988

Overview

Authors:
  1. Matti Vuorinen
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1319)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-XIX
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  2. Conformal geometry

    • Matti Vuorinen
    Pages 1-47

  3. Modulus and capacity

    • Matti Vuorinen
    Pages 48-119

  4. Quasiregular mappings

    • Matti Vuorinen
    Pages 120-172

  5. Boundary behavior

    • Matti Vuorinen
    Pages 173-192

  6. Back Matter

    Pages 193-209
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Keywords

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.

About the author


Bibliographic Information

  • Book Title: Conformal Geometry and Quasiregular Mappings

  • Authors: Matti Vuorinen

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0077904

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-19342-5Published: 01 May 1988

  • eBook ISBN: 978-3-540-39207-1Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XXII, 214

  • Topics: Potential Theory, Differential Geometry

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