Overview

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.

Full Product Details

Author:   Parisa Hariri ,  Riku Klén ,  Matti Vuorinen
Publisher:   Springer Nature Switzerland AG
Imprint:   Springer Nature Switzerland AG
Edition:   1st ed. 2020
Weight:   0.795kg
ISBN:  

9783030320706

ISBN 10:   3030320707
Pages:   502
Publication Date:   26 August 2021
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

Part I: Introduction and Review.- Introduction.- A Survey of QuasiregularMappings.- Part II: Conformal Geometry.- Möbius Transformations.- Hyperbolic Geometry.- Generalized Hyperbolic Geometries.- Metrics and Geometry.- Part III: Modulus and Capacity.- The Modulus of a Curve Family.- The Modulus as a Set Function.- The Capacity of a Condenser.- Conformal Invariants.- Part IV: Intrinsic Geometry.- Hyperbolic Type Metrics.- Comparison of Metrics.- Local Convexity of Balls.- Inclusion Results for Balls.- Part V: QuasiregularMappings.- Basic Properties of QuasiregularMappings.- Distortion Theory.- Dimension-Free Theory.- Metrics and Maps.- Teichmüller’s Displacement Problem.- Part VI: Solutions.- Solutions to Exercises.

Reviews

The book not only provides a reference for the study of quasiregular mappings, but could also serve as a useful handbook for the student/researcher interested in hyperbolic (and hyperbolic-type) metrics on Euclidean domains. ... it constitutes a significant addition to the body of literature on these topics. (David Matthew Freeman, Mathematical Reviews, February, 2022)

Author Information

"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."

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