There has been a great deal of recent interest in the boundary behaviour of conformal maps of the unit disk onto plane domains. This subject which, while embedded in parts of mathematics considered pure, also has very important applications in electrical engineering, fluid dynamics (e.g air current flows around wing profiles etc.). In classical applications of conformal maps, the boundary tended to be smooth: this is not the case in many modern applications (e.g. for Julia sets). Pommerenke's new book gives a comprehensive and up-to-date treatment of this subject in a highly self-contained form, and including many exercises.

Inhalt

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.