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Quasiregular Mappings

  • Seppo Rickman

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 26)

Table of contents

  1. Front Matter
    Pages I-X
  2. Seppo Rickman
    Pages 1-3
  3. Seppo Rickman
    Pages 24-58
  4. Seppo Rickman
    Pages 59-77
  5. Seppo Rickman
    Pages 78-93
  6. Seppo Rickman
    Pages 94-128
  7. Seppo Rickman
    Pages 162-197
  8. Back Matter
    Pages 198-213

About this book

Introduction

Quasiregular Mappings extend quasiconformal theory to the noninjective case.They give a natural and beautiful generalization of the geometric aspects ofthe theory of analytic functions of one complex variable to Euclidean n-space or, more generally, to Riemannian n-manifolds. This book is a self-contained exposition of the subject. A braod spectrum of results of both analytic and geometric character are presented, and the methods vary accordingly. The main tools are the variational integral method and the extremal length method, both of which are thoroughly developed here. Reshetnyak's basic theorem on discreteness and openness is used from the beginning, but the proof by means of variational integrals is postponed until near the end. Thus, the method of extremal length is being used at an early stage and leads, among other things, to geometric proofs of Picard-type theorems and a defect relation, which are some of the high points of the present book.

Keywords

Extremal Length Extremale Länge Länge Nichtlineare Potentialtheorie Nonlinear Potential Theory Potential theory Quasiconformal Mappings Quasikonforme Abbildungen Quasiregular Mappings Quasiregulare Abbildungen Value Distribution Wertverteilung character conformal map manifold

Authors and affiliations

  • Seppo Rickman
    • 1
  1. 1.Department of MathematicsUniversity of HelsinkiHelsinkiFinland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-78201-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-78203-9
  • Online ISBN 978-3-642-78201-5
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site