Overview
- Brings under one roof results previously scattered in many research papers published during the past 50 years since the origin of the three-dimensional theory of quasiconformal and quasiregular mappings
- Contains an extensive set of exercises, including solutions
- Can be used as learning material/collateral reading for several courses
Part of the book series: Springer Monographs in Mathematics (SMM)
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About this book
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.
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Table of contents (20 chapters)
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Front Matter
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Introduction and Review
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Front Matter
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Part II
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Front Matter
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Part IV
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Front Matter
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Part V
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Front Matter
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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)
Authors and Affiliations
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.
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
DOI: https://doi.org/10.1007/978-3-030-32068-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-32067-6Published: 12 April 2020
Softcover ISBN: 978-3-030-32070-6Published: 26 August 2021
eBook ISBN: 978-3-030-32068-3Published: 11 April 2020
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XIX, 502
Number of Illustrations: 56 b/w illustrations
Topics: Potential Theory, Differential Geometry