Displaying similar documents to “A theorem of Semmes and the boundary absolute continuity in all dimensions.”

The boundary absolute continuity of quasiconformal mappings (II).

Juha Heinonen (1996)

Revista Matemática Iberoamericana

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In this paper a quite complete picture is given of the absolute continuity on the boundary of a quasiconformal map B → D, where B is the unit 3-ball and D is a Jordan domain in R with boundary 2-rectifiable in the sense of geometric measure theory. Moreover, examples are constructed, for each n ≥ 3, showing that quasiconformal maps from the unit n-ball onto Jordan domains with boundary (n - 1)-rectifiable need not have absolutely continuous boundary values.

Quasiconformal mappings and Sobolev spaces

Pekka Koskela, Paul MacManus (1998)

Studia Mathematica

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We examine how Poincaré change under quasiconformal maps between appropriate metric spaces having the same Hausdorff dimension. We also show that for many metric spaces the Sobolev functions can be identified with functions satisfying Poincaré, and this allows us to extend to the metric space setting the fact that quasiconformal maps from ℝ Q onto ℝ Q preserve the Sobolev space L 1 , Q ( ℝ Q ) .

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 ≥ 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...

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].

Smooth quasiregular mappings with branching

Mario Bonk, Juha Heinonen (2004)

Publications Mathématiques de l'IHÉS

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We give an example of a 𝒞 3 - ϵ -smooth quasiregular mapping in 3-space with nonempty branch set. Moreover, we show that the branch set of an arbitrary quasiregular mapping in-space has Hausdorff dimension quantitatively bounded away from . By using the second result, we establish a new, qualitatively sharp relation between smoothness and branching.

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.