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On a theorem of Lindelof

Vladimir Ya. Gutlyanskii; Olli Martio; Vladimir Ryazanov — 2011

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

We give a quasiconformal version of the proof for the classical Lindelof theorem: Let $f$ map the unit disk $𝔻$ conformally onto the inner domain of a Jordan curve $𝒞$ : Then $𝒞$ is smooth if and only if arg $f^{'} (z)$ has a continuous extension to $\bar{𝔻}$ . Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.

On conformal dilatation in space.

Bishop, Christopher J.; Gutlyanskiĭ, Vladimir Ya.; Martio, Olli; Vuorinen, Matti — 2003

International Journal of Mathematics and Mathematical Sciences

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