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Zhiguo Chen (2003)
Studia Mathematica
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We characterize affine mappings on the unit disk and on rectangles by module conditions. The main result generalizes the classic Schwarz lemma. As an application, we give a sufficient condition for a K-quasiconformal mapping on a Riemann surface to be a Teichmüller mapping.
Reich, Edgar (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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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.
Pekka Koskela (1994)
Revista Matemática Iberoamericana
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We establish an inverse Sobolev lemma for quasiconformal mappings and extend a weaker version of the Sobolev lemma for quasiconformal mappings of the unit ball of R to the full range 0 < p < n. As an application we obtain sharp integrability theorems for the derivative of a quasiconformal mapping of the unit ball of R in terms of the growth of the mapping.
Kovalev, Leonid V. (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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Luděk Kleprlík (2014)
Open Mathematics
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Let Ω ⊂ ℝn be an open set and X(Ω) be any rearrangement invariant function space close to L q(Ω), i.e. X has the q-scaling property. We prove that each homeomorphism f which induces the composition operator u ↦ u ℴ f from W 1 X to W 1 X is necessarily a q-quasiconformal mapping. We also give some new results for the sufficiency of this condition for the composition operator.
Mayer, Volker (2000)
Annales Academiae Scientiarum Fennicae. Mathematica
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Leonid V. Kovalev, Jani Onninen (2009)
Studia Mathematica
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We obtain improved regularity of homeomorphic solutions of the reduced Beltrami equation, as compared to the standard Beltrami equation. Such an improvement is not possible in terms of Hölder or Sobolev regularity; instead, our results concern the generalized variation of restrictions to lines. Specifically, we prove that the restriction to any line segment has finite p-variation for all p > 1 but not necessarily for p = 1.
Zakeri, Saeed (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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Gong, Jianhua (2008)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Krushkal, Samuel L. (1995)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Matti Vuorinen (1990)
Mathematische Zeitschrift
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Tyutyuev, A.V., Shlyk, V.A. (2004)
Zapiski Nauchnykh Seminarov POMI
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González, María J., Nicolau, Artur (1998)
Annales Academiae Scientiarum Fennicae. Mathematica
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