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Mappings of finite distortion: formation of cusps.

Pekka Koskela, Juhani Takkinen (2007)

Publicacions Matemàtiques

In this paper we consider the extensions of quasiconformal mappings f: B → Ωs to the whole plane, when the domain Ωs is a domain with a cusp of degree s > 0 and thus not an quasidisc. While these mappings do not have quasiconformal extensions, they may have extensions that are homeomorphic mappings of finite distortion with an exponentially integrable distortion, but in such a case ∫2B exp(λK(x)) dx = ∞ for all λ > 1/s. Conversely, for a given s > 0 such a mapping is constructed...

Mappings of finite distortion: sharp Orlicz-conditions.

Janne Kauhanen, Pekka Koskela, Jan Malý, Jani Onninen, Xiao Zhong (2003)

Revista Matemática Iberoamericana

We establish continuity, openness and discreteness, and the condition (N) for mappings of finite distortion under minimal integrability assumptions on the distortion.

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