1549055259-Ubiquitous_Quasidisk__The__Gehring_

Contents

Preface

Part 1. Properties of quasidisks

Chapter 1. Preliminaries

1.1. Quasiconformal mappings

1.2. Modulus of a curve family

1.3. Modulus estimates

1.4. Quasidisks

1.5. What is ahead

Chapter 2. Geometric properties

2.1. Reflection

2.2. The three-point condition

2.3. Reversed triangle inequality

2.4. Linear local connectivity

2.5. Decomposition

Chapter 3. Conformal invariants

3.1. Conformal invariants in a Jordan domain

3.2. Hyperbolic geometry

3.3. Bounds for hyperbolic distance

3.4. Geometry of hyperbolic segments

3.5. Uniform domains

3.6. Min-max property of hyperbolic segments

3.7. Harmonic measure

3.8. Harmonic quasisymmetry

3.9. Harmonic bending

3.10. Quadrilaterals

3.11. Extremal distance property

3.12. Quadrilaterals and harmonic quasisymmetry

Chapter 4. Injectivity criteria
4.1. Meromorphic functions
4.2. Locally bilipschitz mappings
4.3. Locally quasiconformal mappings
4.4. Jacobian of a conformal mapping

Chapter 5. Criteria for extension
5.1. Functions of bounded mean oscillation
5.2. Sobolev and finite energy functions
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