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On a theorem of Lindel fDOI: 10.2478/v10062-011-0012-7 Keywords: Lindel f theorem, infinitesimal geometry, continuous extension to the boundary, differentiability at the boundary, conformal and quaisconformal mappings Abstract: We give a quasiconformal version of the proof for the classical Lindel f 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.
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