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Bloch constants for planar harmonic mappings
Authors:Huaihui Chen   P. M. Gauthier   W. Hengartner
Affiliation:Department of Mathematics, Nanjing Normal University, Nanjing, Jiangsu 210097, People's Republic of China ; Département de mathématiques et de statistique, Université de Montréal, Montréal, Québec, H3C 3J7, Canada ; Département de mathématiques, Université Laval, Québec, G1K 7P4, Canada
Abstract:

We give a lower estimate for the Bloch constant for planar harmonic mappings which are quasiregular and for those which are open. The latter includes the classical Bloch theorem for holomorphic functions as a special case. Also, for bounded planar harmonic mappings, we obtain results similar to a theorem of Landau on bounded holomorphic functions.

Keywords:Bloch constant   harmonic mappings
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