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.

Klappentext

There has been a great deal of recent interest in theboundary behaviour of conformal maps of the unit disk ontoplane domains. In classical applications of conformal maps,the boundary tended to be smooth. This is not the case inmany modern applications (e.g. for Julia sets).The first chapters present basic material and are also ofinterest for people who use conformal mapping as a tool. Thelater chapters deal in greater detail with classicalmaterial and, go into recent developments (e.g. by Makarov).The reader is assumed to know standard complex and realanalysis. The subject of the book is developed from scratchexcept in a few places (e.g. quasiconformal maps) wherethere exist other very goodbooks: in such casesPommerenke's emphasis is on giving additional information.There are over two hundred exercises most of which are easyand meant to test the reader's understanding of the text.Each chapter begins with an overview stating the mainresults informally

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.