%0 Journal Article
%A Gallardo Gutiérrez, Eva Antonia
%A González, María J.
%A Pérez González, Fernando
%A Pommerenke, Christian
%A Rattya, Jouni
%T Locally univalent functions, VMOA and the Dirichlet space
%D 2013
%@ 0024-6115
%U https://hdl.handle.net/20.500.14352/33318
%X 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 1970s. In the case of D, we give a strictly geometric necessary condition for g to satisfy log g'is an element of D, and also offer two different 'semi-geometric' characterizations of when log g'is an element of D.
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