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Loewner chains and quasiconformal extension of holomorphic mappings

Hidetaka Hamada, Gabriela Kohr (2003)

Annales Polonici Mathematici

Let f(z,t) be a Loewner chain on the Euclidean unit ball B in ℂⁿ. Assume that f(z) = f(z,0) is quasiconformal. We give a sufficient condition for f to extend to a quasiconformal homeomorphism of $ℝ^{2 n}$ onto itself.

Lusin's condition (N) and mappings of the class W1, n.

Olli Martio, Jan Maly (1995)

Journal für die reine und angewandte Mathematik

Mappings of domains in $ℝ^{n}$ and their metric tensors.

Reshetnyak, Yu.G. (2003)

Sibirskij Matematicheskij Zhurnal

Mappings of finite distortion: Compactness.

Iwaniec, Tadeusz, Koskela, Pekka, Onninen, Jani (2002)

Annales Academiae Scientiarum Fennicae. Mathematica

Mappings of finite distortion: composition operator.

Hencl, Stanislav, Koskela, Pekka (2008)

Annales Academiae Scientiarum Fennicae. Mathematica

Mappings of finite distortion : discreteness and openness for quasi-light mappings

Stanislav Hencl, Pekka Koskela (2005)

Annales de l'I.H.P. Analyse non linéaire

Mappings of finite distortion: Global homeomorphism theorem.

Holopainen, Ilkka, Pankka, Pekka (2004)

Annales Academiae Scientiarum Fennicae. Mathematica

Mappings of finite distortion: Removability of Cantor sets.

Rajala, Kai (2004)

Annales Academiae Scientiarum Fennicae. Mathematica

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.