Proceedings of the American Mathematical Society

Author(s): Huaihui Chen; P. M. Gauthier; W. Hengartner
Journal: Proc. Amer. Math. Soc. 128 (2000), 3231-3240.
MSC (2000): Primary 30C99; Secondary 30C62
Posted: March 2, 2000
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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.

1.: S. Bochner, Bloch's theorem for real variables, Bull. Amer. Math. Soc. 52 (1946), 715-719. MR 8,204a
2.: D. Bshouty and W. Hengartner, Univalent harmonic mappings in the plane, Ann. Univ. Mariae Curie-Sklodowska Sect. A 48 (1994), 12-42. MR 96m:30025
3.: H. Chen and P. M. Gauthier, On Bloch's constant, J. Anal. Math. 69 (1996), 275-291. MR 97j:30002
4.: E. Heinz, On one-to-one harmonic mappings, Pacific J. Math. 9 (1959), 101-105. MR 21:3683
5.: H. Lewy, On the non-vanishing of the Jacobian in certain one-to-one mappings, Bull. Amer. Math. Soc. 42 (1936), 689-692.
6.: S. Stoïlow, Principes topologiques de la théorie des fonctions analytiques, 1938. Gauthier-Villars.
7.: J. C. Wood, Lewy's theorem fails in higher dimensions, Math. Scand. 69 (1991), 166. MR 93a:58024

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30C99, 30C62

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: 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
Posted: 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 of article: Copyright 2000, American Mathematical Society

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