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© 2020

Conformally Invariant Metrics and Quasiconformal Mappings

Book

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Introduction and Review

    1. Front Matter
      Pages 1-1
    2. Parisa Hariri, Riku Klén, Matti Vuorinen
      Pages 3-5
    3. Parisa Hariri, Riku Klén, Matti Vuorinen
      Pages 7-21
  3. Part II

    1. Front Matter
      Pages 23-23
    2. Parisa Hariri, Riku Klén, Matti Vuorinen
      Pages 25-48
    3. Parisa Hariri, Riku Klén, Matti Vuorinen
      Pages 49-66
    4. Parisa Hariri, Riku Klén, Matti Vuorinen
      Pages 67-81
    5. Parisa Hariri, Riku Klén, Matti Vuorinen
      Pages 83-100
  4. Part III

    1. Front Matter
      Pages 101-102
    2. Parisa Hariri, Riku Klén, Matti Vuorinen
      Pages 103-131
    3. Parisa Hariri, Riku Klén, Matti Vuorinen
      Pages 133-147
    4. Parisa Hariri, Riku Klén, Matti Vuorinen
      Pages 149-172
    5. Parisa Hariri, Riku Klén, Matti Vuorinen
      Pages 173-187
  5. Part IV

    1. Front Matter
      Pages 189-190
    2. Parisa Hariri, Riku Klén, Matti Vuorinen
      Pages 191-208
    3. Parisa Hariri, Riku Klén, Matti Vuorinen
      Pages 209-238
    4. Parisa Hariri, Riku Klén, Matti Vuorinen
      Pages 239-259
    5. Parisa Hariri, Riku Klén, Matti Vuorinen
      Pages 261-278
  6. Part V

    1. Front Matter
      Pages 279-279

About this book

Introduction

This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key role throughout the whole book. The intended readership consists of mathematicians from beginning graduate students to researchers. The prerequisite requirements are modest: only some familiarity with basic ideas of real and complex analysis is expected.

Keywords

Möbius transformations Quasiconformal mappings in the plane Quasiregular mappings in Rn conformal invariants boundary properties of QR-maps hyperbolic metric

Authors and affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland
  2. 2.Turku PET CentreUniversity of TurkuTurkuFinland
  3. 3.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland

About the authors

Matti Vuorinen, currently professor of mathematics at the University of Turku and docent at the University of Helsinki, is the author of more than 200 publications, including 2 books on quasiregular and quasiconformal mappings. The first entitled "Conformal geometry and quasiregular mappings" (Lecture Notes in Math. Vol. 1319) was published by Springer-Verlag in 1988 and the second, entitled "Conformal invariants, inequalities and quasiconformal mappings" by J. Wiley, in 1997.

Riku Klén, currently assistant professor at the University of Turku, Turku PET Centre, does research in Conformal Geometry and Quasiconformal Mappings as well as Medical Imaging.

Parisa Hariri, obtained her PhD in Mathematics from the University of Turku in 2018, under the supervision of Matti Vuorinen and Riku Klen. Her PhD thesis was on 'Hyperbolic Type Metrics in Geometric Function Theory'. She is currently working as medical statistician at the University of Oxford Vaccine Group in the Department of Paediatrics.


Bibliographic information

  • Book Title Conformally Invariant Metrics and Quasiconformal Mappings
  • Authors Parisa Hariri
    Riku Klén
    Matti Vuorinen
  • Series Title Springer Monographs in Mathematics
  • Series Abbreviated Title Springer Monographs in Mathematics
  • DOI https://doi.org/10.1007/978-3-030-32068-3
  • Copyright Information Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-030-32067-6
  • Softcover ISBN 978-3-030-32070-6
  • eBook ISBN 978-3-030-32068-3
  • Series ISSN 1439-7382
  • Series E-ISSN 2196-9922
  • Edition Number 1
  • Number of Pages XIX, 502
  • Number of Illustrations 56 b/w illustrations, 0 illustrations in colour
  • Topics Potential Theory
    Differential Geometry
  • Buy this book on publisher's site