Mappings of Finite Distortion : Formation of Cusps

@inproceedings{Koskela2007MappingsOF,
title={Mappings of Finite Distortion : Formation of Cusps},
author={Pekka Koskela and Juhani Takkinen},
year={2007}
}

Suppose that f is a quasiconformal mapping of the unit disc B into R. It is well-known that f has an extension to a quasiconformal homeomorphism of the entire plane if and only if the boundary of f(B) is a quasicircle. Since quasicircles are exactly the Jordan curves which satisfy the so-called three point condition, the extendability of f to a quasiconformal mapping of the entire plane is determined by the geometric properties of the boundary of f(B). For this see [2]. On the other hand, a… CONTINUE READING