Boundary Behaviour of Conformal Maps
By: by Christian Pommerenke
Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics -- 299; Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics -- 299
Publisher: Springer Berlin Heidelberg
Published: 1992
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 300
ISBN-13: 9783642081293; 9783662027707
Subjects: Mathematics; Functions of complex variables
Description: There has been a great deal of recent interest in the boundary behaviour of conformal maps of the unit disk onto plane domains. 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). The first chapters present basic material and are also of interest for people who use conformal mapping as a tool. The later chapters deal in greater detail with classical material and, go into recent developments (e.g. by Makarov). The reader is assumed to know standard complex and real analysis. The subject of the book is developed from scratch except in a few places (e.g. quasiconformal maps) where there exist other very goodbooks: in such cases Pommerenke's emphasis is on giving additional information. There are over two hundred exercises most of which are easy and meant to test the reader's understanding of the text. Each chapter begins with an overview stating the main results informally.
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