**University Lecture Series**

Volume: 54;
2010;
143 pp;
Softcover

MSC: Primary 30; 28;

Print ISBN: 978-0-8218-5229-3

Product Code: ULECT/54

List Price: $44.00

Individual Member Price: $35.20

**Electronic ISBN: 978-1-4704-1649-2
Product Code: ULECT/54.E**

List Price: $44.00

Individual Member Price: $35.20

#### Supplemental Materials

# Conformal Dimension: Theory and Application

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*John M. Mackay; Jeremy T. Tyson*

Conformal dimension measures the extent to which the Hausdorff dimension of a metric space can be lowered by quasisymmetric deformations. Introduced by Pansu in 1989, this concept has proved extremely fruitful in a diverse range of areas, including geometric function theory, conformal dynamics, and geometric group theory.

This survey leads the reader from the definitions and basic theory through to active research applications in geometric function theory, Gromov hyperbolic geometry, and the dynamics of rational maps, amongst other areas. It reviews the theory of dimension in metric spaces and of deformations of metric spaces. It summarizes the basic tools for estimating conformal dimension and illustrates their application to concrete problems of independent interest. Numerous examples and proofs are provided.

Working from basic definitions through to current research areas, this book can be used as a guide for graduate students interested in this field, or as a helpful survey for experts. Background needed for a potential reader of the book consists of a working knowledge of real and complex analysis on the level of first- and second-year graduate courses.

#### Table of Contents

# Table of Contents

## Conformal Dimension: Theory and Application

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface ix10 free
- List of figures xiii14 free
- Background material 116 free
- Conformal gauges and conformal dimension 2136
- Gromov hyperbolic groups and spaces and their boundaries 2540
- Lower bounds for conformal dimension 4964
- Sets and spaces of conformal dimension zero 6782
- Gromov–Hausdorff tangent spaces and conformal dimension 7994
- Ahlfors regular conformal dimension 91106
- Global quasiconformal dimension 107122
- Back Cover Back Cover1162

#### Readership

Graduate students and research mathematicians interested in geometric function theory.