Bloch constants for planar harmonic mappings
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- by Huaihui Chen, P. M. Gauthier and W. Hengartner PDF
- Proc. Amer. Math. Soc. 128 (2000), 3231-3240 Request permission
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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3231-3240
- MSC (2000): Primary 30C99; Secondary 30C62
- DOI: https://doi.org/10.1090/S0002-9939-00-05590-8
- MathSciNet review: 1707142