A distortion theorem for quasiconformal mappings

Michel Zinsmeister

Displaying similar documents to “A distortion theorem for quasiconformal mappings”

An inverse Sobolev lemma.

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.

Quasiregular mappings of maximal local modulus of continuity.

Kovalev, Leonid V. (2004)

Annales Academiae Scientiarum Fennicae. Mathematica

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Eine Klasse nichtschlichter konformer Abbildungen mit einer schlichten quasikonformen Fortsetzung. II

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.

Quasiconformal mappings with Sobolev boundary values

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 $ℝ_{+}^{n + 1}$ of $ℝ^{n + 1}$ , $n \geq 2$ , whose almost everywhere defined trace in $ℝ^{n}$ has distributional differential in $L^{n} (ℝ^{n})$ . We give both geometric and analytic characterizations for this possibility, resembling the situation in the classical Hardy space $H^{1}$ . More generally, we consider certain positive functions defined on $ℝ_{+}^{n + 1}$ , called conformal densities. These densities mimic the averaged derivatives of quasiconformal mappings, and we prove analogous trace theorems...

Composition operators on W 1 X are necessarily induced by quasiconformal mappings

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.