DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC Dn

doi:10.1016/S0252-9602(10)60159-2

Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (5): 1661-1668.doi: 10.1016/S0252-9602(10)60159-2

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DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC Dⁿ

WANG Jian-Fei¹, LIU Ta-Shun², TANG Xiao-Min²

1.College of Mathematics Physics and |Information Engineering, Zhejiang Normal University, Jinhua 321004, China; 2.Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China

Received:2008-03-18 Revised:2008-11-19 Online:2010-09-20 Published:2010-09-20
Supported by:
The work was partly supported by the National Natural Science Foundation of China (10826083, 10971063), NSF of Zhejiang Province (D7080080, Y606197, Y6090694) and Scientific Research Fund of Zhejiang Provincial Education Department (Y200805520).

Abstract

Abstract:

In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc Dⁿwith critical points, which extend the results of Liu and Minda to higher dimensions. We obtain lower bounds of |det (f'(z))| and R det (f'(z)) for Bloch mapping f. As an application, some lower and upper bounds of Bloch constants for the subfamilies of holomorphic mappings are given.

Key words: Bloch constant, Bloch mapping, critical point, holomorphic mapping

CLC Number:

32H02

WANG Jian-Fei, LIU Ta-Shun, TANG Xiao-Min. DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC Dⁿ[J].Acta mathematica scientia,Series B, 2010, 30(5): 1661-1668.

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DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC Dⁿ

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