Boundary Behaviour of Conformal Maps is popular PDF and ePub book, written by Christian Pommerenke in 2013-04-09, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Boundary Behaviour of Conformal Maps can be Read Online from any device for your convenience.
Boundary Behaviour of Conformal Maps Book PDF Summary
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.
Detail Book of Boundary Behaviour of Conformal Maps PDF
- Author : Christian Pommerenke
- Release : 09 April 2013
- Publisher : Springer Science & Business Media
- ISBN : 9783662027707
- Genre : Mathematics
- Total Page : 307 pages
- Language : English
- PDF File Size : 13,7 Mb
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