Univalent harmonic mappings into two-slit domains

Andrzej Ganczar, Jarosław Widomski

Abstract


We study some classes of planar harmonic mappings produced with the shear construction devised by Clunie and Sheil-Small in 1984. The first section reviews the basic concepts and describes the shear construction. The main body of the paper deals with the geometry of the classes constructed.

doi:10.1017/S1446788709000391

Keywords


univalent harmonic mappings, shear construction



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Journal of the Austral. Maths Soc, copyright Australian Mathematical Society.