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Quasiconformal Surgery in Holomorphic Dynamics by Núria Fagella, Bodil Branner

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1

Quasiconformal geometry

Since its introduction in the early 1980s quasiconformal surgery has become a major tool in the development of the theory of holomorphic dynamics.

The goal of this chapter is to collect the basic definitions and results about quasiconformal mappings used in surgery, and those necessary to make a coherent description. We give a geometrical and analytical approach and give precise references to important results in the vast literature about quasiconformal mappings. In general we only prove those we could not find proven elsewhere, even if simple. However, since the Integrability Theorems (Theorems 1.27 and 1.28), also called the Measurable Riemann Mapping Theorems, are the cornerstone behind every surgery construction ...

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