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Quasiconformal Surgery in Holomorphic Dynamics by Núria Fagella, Bodil Branner

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2

Boundary behaviour of quasiconformal maps: extensions and interpolations

In surgery constructions we often need to interpolate (quasiconformally) between two different maps defined on distinct regions of the plane. This involves finding quasiconformal extensions of given boundary maps, whenever possible, but also knowing whether a map defined on a certain domain extends continuously to its boundary. We address these two types of problems in this chapter.

We recall some elementary definitions about curves and their regularity (see [Pom] for details and proofs). A curve γ in the complex plane is the image set of a parametric representation or parametrization. In the following we use γ both as a name for a continuous function parametrizing the ...

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