Conformally Invariant Metrics and Quasiconformal Mappings

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.

List 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.

About the author

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.

Report

"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)

Product details

Authors	Paris Hariri, Parisa Hariri, Rik Klén, Riku Klén, Matti Vuorinen
Publisher	Springer, Berlin
Languages	English
Product format	Paperback / Softback
Released	26.04.2021
EAN	9783030320706
ISBN	978-3-0-3032070-6
No. of pages	502
Dimensions	155 mm x 27 mm x 235 mm
Illustrations	XIX, 502 p. 56 illus.
Series	Springer Monographs in Mathematics
Subject	Natural sciences, medicine, IT, technology > Mathematics > Analysis

Product details

• Authors: Paris Hariri, Parisa Hariri, Rik Klén, Riku Klén, Matti Vuorinen
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 26.04.2021
• EAN: 9783030320706
• ISBN: 978-3-0-3032070-6
• No. of pages: 502
• Dimensions: 155 mm x 27 mm x 235 mm
• Illustrations: XIX, 502 p. 56 illus.
• Series: Springer Monographs in Mathematics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis