Continuously removable sets for quasiconformal mappings.
Tyutyuev, A.V., Shlyk, V.A. (2004)
Zapiski Nauchnykh Seminarov POMI
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Displaying similar documents to “On certain functional equations for quasiconformal mappings”
Continuously removable sets for quasiconformal mappings.
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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.
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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.
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