Conformally Invariant Metrics and Quasiconformal Mappings
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 confo...
| Main Authors: | , , |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2020, 2020
|
| Edition: | 1st ed. 2020 |
| Series: | Springer Monographs in Mathematics
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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