Conformally Invariant Metrics and Quasiconformal Mappings
Authors: Hariri, Parisa, Klen, Riku, Vuorinen, Matti
Free Preview- 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
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- About this book
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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.
- About the authors
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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.
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.
- Table of contents (20 chapters)
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Introduction
Pages 3-5
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A Survey of Quasiregular Mappings
Pages 7-21
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Möbius Transformations
Pages 25-48
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Hyperbolic Geometry
Pages 49-66
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Generalized Hyperbolic Geometries
Pages 67-81
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Table of contents (20 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Conformally Invariant Metrics and Quasiconformal Mappings
- Authors
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- Parisa Hariri
- Riku Klen
- Matti Vuorinen
- Series Title
- Springer Monographs in Mathematics
- Copyright
- 2020
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-32068-3
- DOI
- 10.1007/978-3-030-32068-3
- Hardcover ISBN
- 978-3-030-32067-6
- Series ISSN
- 1439-7382
- Edition Number
- 1
- Number of Pages
- XIX, 502
- Number of Illustrations
- 56 b/w illustrations
- Topics
