Boundary Behaviour of Conformal Maps (Paperback, Softcover reprint of hardcover 1st ed. 1992)

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."

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Grundlehren der mathematischen Wissenschaften, 299
Release date:	December 2010
First published:	1992
Authors:	Christian Pommerenke
Dimensions:	235 x 155 x 16mm (L x W x T)
Format:	Paperback
Pages:	300
Edition:	Softcover reprint of hardcover 1st ed. 1992
ISBN-13:	978-3-642-08129-3
Categories:	Books > Science & Mathematics > Science: general issues > Scientific standards Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
LSN:	3-642-08129-0
Barcode:	9783642081293

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