On a parametric method for conformal maps with quasiconformal extensions.
Vasil'ev, Alexander (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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Vasil'ev, Alexander (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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Alexander Vasilev (2004)
Publications de l'Institut Mathématique
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Tyson, Jeremy (1998)
Annales Academiae Scientiarum Fennicae. Mathematica
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Reiner Kühnau (2011)
Annales UMCS, Mathematica
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We study a dual analogue of the class Σ(κ) of hydrodynamically normalized schlicht conformal mappings g(z) of the exterior of the unit circle with a [...] -quasiconformal extension, namely now those (non-schlicht) mappings g(z) for which g(z) has such a quasiconformal extension.
Zorich, V.A. (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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Martin Chuaqui, Brad Osgood (1992)
Mathematische Annalen
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Pekka Tukia, Jussi Väisälä (1984)
Mathematische Annalen
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Jan G. Krzyż (1987)
Colloquium Mathematicae
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Bruce H. Hanson (1994)
Mathematica Scandinavica
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Kevin M. Pilgrim (2004)
Fundamenta Mathematicae
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Let Q be the unit square in the plane and h: Q → h(Q) a quasiconformal map. When h is conformal off a certain self-similar set, the modulus of h(Q) is bounded independent of h. We apply this observation to give explicit estimates for the variation of multipliers of repelling fixed points under a "spinning" quasiconformal deformation of a particular cubic polynomial.
Michel Zinsmeister (1986)
Bulletin de la Société Mathématique de France
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Miyachi, Hideki (2007)
Annales Academiae Scientiarum Fennicae. Mathematica
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Vladimir Gutlyanskii, Olli Martio, Vladimir Ryazanov (2011)
Annales UMCS, Mathematica
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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.
Keith Carne (1990)
Journal für die reine und angewandte Mathematik
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Reich, Edgar (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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Rohde, S. (1997)
Annales Academiae Scientiarum Fennicae. Mathematica
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