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

Format:

Book

Author/Creator:

Hariri, Parisa, author.

Klén, Riku, author.

Vuorinen, Matti, author.

Series:

Springer monographs in mathematics

Springer Monographs in Mathematics

Language:

English

Subjects (All):

Quasiconformal mappings.

Functions of several complex variables.

Geometry, Differential.

Potential theory (Mathematics).

Physical Description:

xix, 502 pages: illustrations; 24cm.

Place of Publication:

Cham: Springer International Publishing, [2020].

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.

Contents:

A survey of quasiregular mapping

Conformal geometry

Möbius transformations

Hyperbolic geometry

Generalized hyperbolic geometries

Metrics and geometry

Modulus and capacity

The modulus of a curve family

The modulus as a set function

The capacity of a condenser

Conformal invariants

Intrinsic geometry

Hyperbolic type metrics

Comparison of metrics

Local convexity of balls

Inclusion results for balls

Quasiregular mappings

Basic properties of quasiregular mappings

Distortion theory

Dimension-free theory

Metrics and maps

Teichmüller's displacement problem

Solutions to exercises.

Notes:

Includes bibliographical references (pages 469-492) and index.

ISBN:

3030320677

9783030320676

OCLC:

1114745112