
Boundary Behaviour of Conformal Maps
Christian Pommerenke(Author)
Springer (Publisher)
Published on 7. December 2010
Book
Paperback/Softback
IX, 300 pages
978-3-642-08129-3 (ISBN)
Description
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 applications of conformal mapping, the domain is bounded by a piecewise smooth curve. In many recent applications however, the domain has a very bad boundary. It may have nowhere a tangent as is the case for Julia sets. Then the conformal map has many unexpected properties, for instance almost all the boundary is mapped onto almost nothing and vice versa. The book is meant for two groups of users. (1) Graduate students and others who, at various levels, want to learn about conformal mapping. Most sections contain exercises to test the understand ing. They tend to be fairly simple and only a few contain new material. Pre requisites are general real and complex analyis including the basic facts about conformal mapping (e.g. AhI66a). (2) Non-experts who want to get an idea of a particular aspect of confor mal mapping in order to find something useful for their work. Most chapters therefore begin with an overview that states some key results avoiding tech nicalities. The book is not meant as an exhaustive survey of conformal mapping. Several important aspects had to be omitted, e.g. numerical methods (see e.g.
More details
Series
Edition
1st ed. Softcover of orig. ed. 1992
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
IX, 300 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 17 mm
Weight
476 gr
ISBN-13
978-3-642-08129-3 (9783642081293)
DOI
10.1007/978-3-662-02770-7
Schweitzer Classification
Other editions
Additional editions

Christian Pommerenke
Boundary Behaviour of Conformal Maps
Book
08/1992
Springer
€117.69
Shipment within 7-9 days
Content
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.