Conformally Invariant Metrics and Quasicon...

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2021
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	524
Reihe:	Springer Monographs in Mathematics
Inhalt:	xix 502 S. 56 s/w Illustr. 502 p. 56 illus.
ISBN-13:	9783030320706
ISBN-10:	3030320707
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Hariri, Parisa Vuorinen, Matti Klén, Riku
Auflage:	1st ed. 2020
Hersteller:	Springer International Publishing Springer Monographs in Mathematics
Maße:	235 x 155 x 29 mm
Von/Mit:	Parisa Hariri (u. a.)
Erscheinungsdatum:	26.08.2021
Gewicht:	0,785 kg

preigu-id: 119731982