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Estimates on Bloch constants for planar harmonic mappings. (English) Zbl 1196.30020
The author gives estimates of the Bloch constants for quasiregular harmonic mappings and open planar harmonic mappings. The results, presented in the paper, improve the ones made by {\it H. Chen, P. M. Gauthier} and {\it W. Hengartner} [Proc. Am. Math. Soc. 128, No.11, 3231--3240 (2000; Zbl 0956.30012)] and {\it A. Grigoryan} [Complex Var. Elliptic Equ. 51, No. 1, 81--87 (2006; Zbl 1114.30024)].

30C62Quasiconformal mappings in the plane
31A05Harmonic, subharmonic, superharmonic functions (two-dimensional)
Full Text: DOI
[1] Lewy H. On the non-vanishing of the Jacobian in certain one-to-one mappings. Bull Amer Math Soc, 42: 689--692 (1936) · Zbl 62.0555.01 · doi:10.1090/S0002-9904-1936-06397-4
[2] Chen H H. On the Bloch constant. In: Arakelian N, Gauthier P M, eds. Approximation, Complex Analysis, and Potential Theory. Dordrecht: KLuwer Acad Publ, 2001, 129--161 · Zbl 1001.30028
[3] Laudau E. Der Picard-Schottysche Satz und die Blochsche Konstanten. Berlin: Sitzungsber Press Akad Wiss Berlin Phys-Math Kl, 1926, 467--474
[4] Chen H H, Gauthier P M, Hengartner W. Bloch constants for planar harmonic mappings. Proc Amer Math Soc, 128: 3231--3240 (2000) · Zbl 0956.30012 · doi:10.1090/S0002-9939-00-05590-8
[5] Graham I, Kohr G. Geometric Function Theory in One and Higher Dimensions. New York: Marcel Dekker Inc, 2003 · Zbl 1042.30001
[6] Dorff M, Nowak M. Landau’s theorem for planar harmonic mappings. Comput Methods Funct Theory, 4(1): 151--158 (2000) · Zbl 1060.30033
[7] Grigoryan A. Landau and Bloch theorems for harmonic mappings. Complex Variable Theory Appl, 51(1): 81--87 (2006) · Zbl 1114.30024 · doi:10.1080/02781070500369214
[8] Huang X Z. Estimates on Bloch constants for planar harmonic mappings. J Math Anal Appl, 337: 880--887 (2007) · Zbl 1142.31001
[9] Chen H H, Xiong C J. Julia’s lemma and Bloch constants. Sci China Ser A-Math, 46(3): 326--332 (2003) · Zbl 1217.30049
[10] Kuang J C. Applied Inequalities, 3nd ed. Jinan: Shandong Science and Technology Press, 2004