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Field name	Details
Dewey Class	515.9
Title	Boundary Behaviour of Conformal Maps ([EBook] /) / by Christian Pommerenke.
Author	Pommerenke, Christian
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1992.
Physical Details	IX, 300 p. : online resource.
Series	Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 0072-7830 ; ; 299
ISBN	9783662027707
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-02770-7
Links to Related Works	Subject References: Functions of a Complex Variable . Functions of complex variables . Mathematics . Measurement . Measurement Science and Instrumentation . Physical measurements . Authors: Pommerenke, Christian . Corporate Authors: SpringerLink (Online service) . Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics . Classification: 515.9 .

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Boundary Behaviour of Conformal Maps

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