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On a theorem of Lindelöf

Vladimir Gutlyanskii;  Olli Martio;  Vladimir Ryazanov — 2011

Annales UMCS, Mathematica

We give a quasiconformal version of the proof for the classical Lindelöf 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 arh f'(z) has a continuous extension to D. Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.

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 𝔻 ¯ . Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.

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