1549055259-Ubiquitous_Quasidisk__The__Gehring_

The Ubiquitous Quasidisk ...

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Mathematical Surveys and Monographs Volume 184 The Ubiquitous Quasidisk Frederick W. Gehring Kari Hag With contributions by Ole ...

EDITORIAL COMMITTEE Ralph L. Cohen, Chair Michael A. Singer Benjamin Sudakov Michael I. Weinstein 2010 Mathematics Subject Class ...

To Lois ...

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Contents Preface Part 1. Properties of quasidisks Chapter 1. Preliminaries 1.1. Quasiconformal mappings 1.2. Modulus of a curve ...

v iii 5.3. Quasiconformal mappings 5.4. Bilipschitz mappings CONTENTS Chapter 6. Two-sided criteria 6.1. Linear local connectivi ...

Bibliography Index CONTENTS ix 163 169 ...

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Preface In August 1981 the first author gave a short course of six lectures on function theory at the NATO Advanced Study Instit ...

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Part 1 Properties of quasidisks ...

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CHAPTER 1 Preliminaries We collect here some definitions and properties of plane quasiconformal map- pings. Two basic references ...

4 1. PRELIMINARIES z f FIGURE 1. DEFINITION 1.1.3. A homeomorphism f : D---+ D' is K-quasiconformal where 1 :SK< oo if H1(z) ...

1.1. QUASICONFORMAL MAPPINGS 5 (1.1.2) was not required to hold by a set of measure zero and then by requiring that f preserves ...

6 1. PRELIMINARIES If f : D-t D' and g : D'---+ D" are both sense-preserving and quasiconformal, then μ 901 = μ! a.e. in D if an ...

1.3. MODULUS ESTIMATES Thus p E adm(r), whence mod(r):::; r p(z)^2 dm = r p'(f(z))^2 lf'(z)l^2 dm JR2 JD = r p'(w)^2 dm:::; r p' ...

8 1. PRELIMINARIES i a+i R 0 a FIGURE 1. for 0 < x < a. Thus L 2 p(z) 2 dm 21a ( 1 p(x + iy) 2 dy) dx 2 a and Next the fun ...