Displaying similar documents to “On a paper of Carleson.”

On conformal dilatation in space.

Bishop, Christopher J., Gutlyanskiĭ, Vladimir Ya., Martio, Olli, Vuorinen, Matti (2003)

International Journal of Mathematics and Mathematical Sciences

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On local injectivity and asymptotic linearity of quasiregular mappings

V. Gutlyanskiĭ, O. Martio, V. Ryazanov, M. Vuorinen (1998)

Studia Mathematica

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It is shown that the approximate continuity of the dilatation matrix of a quasiregular mapping f at x 0 implies the local injectivity and the asymptotic linearity of f at x 0 . Sufficient conditions for l o g | f ( x ) - f ( x 0 ) | to behave asymptotically as l o g | x - x 0 | are given. Some global injectivity results are derived.

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...

On a theorem of Lindelöf

Vladimir Gutlyanskii, Olli Martio, Vladimir Ryazanov (2011)

Annales UMCS, Mathematica

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We give a quasiconformal version of the proof for the classical Lindelöf theorem: Let f map the unit disk D conformally onto the inner domain of a Jordan curve C. Then C is smooth if and only if arh f'(z) has a continuous extension to D. Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.