Boundary Behaviour of Conformal Maps

There has been a great deal of recent interest in the boundary behavior 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 pre [...]
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There has been a great deal of recent interest in the boundary behavior 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. quasi conformal maps) where there exist other very good books: 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.