�ber die quasikonforme Fortsetzung schlichter Funktionen

“…One of the geometric characterizations of these BMOA-domains immediately gives their bi-Lipschitz invariance, a property which a priori is far from being obvious. For characterizations in terms of the Schwarzian derivative of when log g ′ belongs either to D, VMOA or B 0 , we refer to [3] and [18].…”

Section: Introduction and Resultsmentioning

confidence: 99%

Locally univalent functions, VMOA and the Dirichlet space

Gallardo-Gutiérrez

González

Pérez-González

et al. 2012

Proceedings of the London Mathematical Society

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Abstract. We study geometric properties of the image of the unit circle under a bounded locally univalent function g such that log g ′ belongs either to the Dirichlet space D, VMOA or the little Bloch space B 0 . Concerning VMOA and B 0 , our findings generalize the corresponding results for conformal maps shown by Pommerenke in the late seventies. In the case of D, we give a strictly geometric necessary condition for g to satisfy log g ′ ∈ D, and also offer two different "semi-geometric" characterizations of when log g ′ ∈ D.

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“…A characterization of asymptotically conformal curves in terms of quasiconformal mappings will be given in [2].…”

Section: (Z-~)g'(~)mentioning

confidence: 99%