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.
€117.69
Table of Content
Part I: Introduction and Review.- Introduction.- A Survey of Quasiregular Mappings.- 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: Quasiregular Mappings.- Basic Properties of Quasiregular Mappings.- 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 Ph D in Mathematics from the University of Turku in 2018, under the supervision of Matti Vuorinen and Riku Klen. Her Ph D 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.
Language English ● Format PDF ● Pages 502 ● ISBN 9783030320683 ● File size 8.8 MB ● Publisher Springer International Publishing ● City Cham ● Country CH ● Published 2020 ● Downloadable 24 months ● Currency EUR ● ID 7435502 ● Copy protection Social DRM
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