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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bloch constants for planar harmonic mappings


Authors: Huaihui Chen, P. M. Gauthier and W. Hengartner
Journal: Proc. Amer. Math. Soc. 128 (2000), 3231-3240
MSC (2000): Primary 30C99; Secondary 30C62
Published electronically: March 2, 2000
MathSciNet review: 1707142
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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.


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Additional Information

Huaihui Chen
Affiliation: Department of Mathematics, Nanjing Normal University, Nanjing, Jiangsu 210097, People’s Republic of China
Email: hhchen@njnu.edu.cn

P. M. Gauthier
Affiliation: Département de mathématiques et de statistique, Université de Montréal, Montréal, Québec, H3C 3J7, Canada
Email: gauthier@dms.umontreal.ca

W. Hengartner
Affiliation: Département de mathématiques, Université Laval, Québec, G1K 7P4, Canada
Email: walheng@mat.ulaval.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05590-8
PII: S 0002-9939(00)05590-8
Keywords: Bloch constant, harmonic mappings
Received by editor(s): December 14, 1998
Published electronically: March 2, 2000
Additional Notes: This research was supported in part by NSFC(China), NSERC(Canada) and FCAR(Québec).
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2000 American Mathematical Society