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Conformally invariant metrics and quasiconformal mappings / Parisa Hariri, Riku Klén, Matti Vuorinen.

Hairi, Parisa.; Klén, Riku.; Vuorinen, Matti.
2020
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Title
Conformally invariant metrics and quasiconformal mappings / Parisa Hariri, Riku Klén, Matti Vuorinen.
Author
Hairi, Parisa.
ISBN
9783030320683 (electronic book)
3030320685 (electronic book)
9783030320676
3030320677
DOI
https://doi.org/10.1007/978-3-030-32
Publication Details
Cham : Springer, 2020.
Language
English
Description
1 online resource
Item Number
10.1007/978-3-030-32
Call Number
QA360
Dewey Decimal Classification
511.3/26
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Added Author
Klén, Riku.
Vuorinen, Matti.
Series
Springer monographs in mathematics.
Available in Other Form
Print version: 9783030320676
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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
Teichmüllers Displacement Problem
Part VI: Solutions
Solutions to Exercises.

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