Boundary Behaviour of Conformal Maps

• Main Author: Pommerenke, Christian
• Format: eBook
• Language: English
• Published: Berlin, Heidelberg Springer Berlin / Heidelberg 1992; Springer Berlin Heidelberg
• Edition: 1
• Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
• Subjects: Conformal mapping; Functions of a Complex Variable; Functions of complex variables; Mathematics; Mathematics and Statistics; Measurement Science and Instrumentation

We study the boundary behaviour of a conformal map of the unit disk onto an arbitrary simply connected plane domain. A principal aim of the theory is to obtain a one-to-one correspondence between analytic properties of the function and geometrie properties of the domain. In the classical application...

Table of Contents:

• Grundlehren der mathematischen Wissenschaften 299 -- Boundary Behaviour of Conformal Maps -- Copyright -- Preface -- Contents -- Chapter 1. Some Basic Facts -- Chapter 2. Continuity and Prime Ends -- Chapter 3. Smoothness and Corners -- Chapter 4. Distortion -- Chapter 5. Quasidisks -- Chapter 6. Linear Measure -- Chapter 7. Smirnov and Lavrentiev Domains -- Chapter 8. Integral Means -- Chapter 9. Curve Families and Capacity -- Chapter 10. Hausdorff Measure -- Chapter 11. Local Boundary Behaviour -- References -- Author Index -- Subject Index
• 1. Some Basic Facts -- 2. Continuity and Prime Ends -- 3. Smoothness and Corners -- 4. Distortion -- 5. Quasidisks -- 6. Linear Measure -- 7. Smirnov and Lavrentiev Domains -- 8. Integral Means -- 9. Curve Families and Capacity -- 10. Hausdorff Measure -- 11. Local Boundary Behaviour -- References -- Author Index.