Conformally Invariant Metrics and Quasiconformal Mappings - Parisa Hariri, Riku Klén, Matti Vuorinen

Conformally Invariant Metrics and Quasiconformal Mappings

Buch | Hardcover
XIX, 502 Seiten
2020 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-32067-6 (ISBN)
128,39 inkl. MwSt
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.

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.

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.

"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)

“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)

Erscheinungsdatum
Reihe/Serie Springer Monographs in Mathematics
Zusatzinfo XIX, 502 p. 56 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 945 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte boundary properties of QR-maps • conformal invariants • hyperbolic metric • Möbius transformations • Quasiconformal mappings in the plane • Quasiregular mappings in Rn
ISBN-10 3-030-32067-7 / 3030320677
ISBN-13 978-3-030-32067-6 / 9783030320676
Zustand Neuware
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