The boundary absolute continuity of quasiconformal mappings (II).

Juha Heinonen

Displaying similar documents to “The boundary absolute continuity of quasiconformal mappings (II).”

A theorem of Semmes and the boundary absolute continuity in all dimensions.

Juha Heinonen (1996)

Revista Matemática Iberoamericana

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We use a recent theorem of Semmes to resolve some questions about the boundary absolute continuity of quasiconformal maps in space.

On boundary correspondence under quasiconformal mappings.

Gutlyanskij, V.Ya., Ryazanov, V.I. (1996)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

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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...

David maps and Hausdorff dimension.

Zakeri, Saeed (2004)

Annales Academiae Scientiarum Fennicae. Mathematica

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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.

Quasiconformal mappings onto John domains.

Juha Heinonen (1989)

Revista Matemática Iberoamericana

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In this paper we study quasiconformal homeomorphisms of the unit ball B = B = {x ∈ R: |x| < 1} of R onto John domains. We recall that John domains were introduced by F. John in his study of rigidity of local quasi-isometries [J]; the term John domain was coined by O. Martio and J. Sarvas seventeen years later [MS]. From the various equivalent characterizations we shall adapt the following definition based on diameter carrots, cf. [V4], [V5], [NV].

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.

A boundary value problem for Beltrami differential equation

Keiichi Shibata (1996)

Banach Center Publications

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Solutions to Beltrami differential equation with prescribed boundary correspondence in some plane domains are given.

Hölder spaces of quasiconformal mappings.

Kovalev, Leonid V. (2004)

Publications de l'Institut Mathématique. Nouvelle Série

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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.