On a class of extremal quasi-conformal mappings
Kenneth P. Goldberg (1976)
Annales Polonici Mathematici
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Kenneth P. Goldberg (1976)
Annales Polonici Mathematici
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Olli Lehto (1976)
Annales Polonici Mathematici
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Petru Caraman (1976)
Annales Polonici Mathematici
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J. Ławrynowicz (1969)
Annales Polonici Mathematici
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G. D. Mostow (1968)
Publications Mathématiques de l'IHÉS
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Zorich, V.A. (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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Dyn'kin, Evsey (1997)
Annales Academiae Scientiarum Fennicae. Mathematica
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G. Opfer (1980)
Numerische Mathematik
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Frederick Gehring (1999)
Banach Center Publications
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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.
Ken'ichi Ohshika (1989)
Mathematische Zeitschrift
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Klaus Menke (1985)
Annales Polonici Mathematici
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Michel Zinsmeister (1986)
Bulletin de la Société Mathématique de France
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Kari Astala, Mario Bonk, Juha Heinonen (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We consider quasiconformal mappings in the upper half space of , , whose almost everywhere defined trace in has distributional differential in . We give both geometric and analytic characterizations for this possibility, resembling the situation in the classical Hardy space . More generally, we consider certain positive functions defined on , called conformal densities. These densities mimic the averaged derivatives of quasiconformal mappings, and we prove analogous trace theorems...