Displaying similar documents to “The Differential of a Quasi-conformal Mapping of a Carnot-Caratheodry Space.”

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.

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 + n + 1 of n + 1 , n 2 , whose almost everywhere defined trace in n has distributional differential in L n ( 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 + n + 1 , called conformal densities. These densities mimic the averaged derivatives of quasiconformal mappings, and we prove analogous trace theorems...