DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC Dn

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

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1661-1668.doi: 10.1016/S0252-9602(10)60159-2

DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC Dⁿ

王建飞¹, 刘太顺², 唐笑敏²

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

收稿日期:2008-03-18 修回日期:2008-11-19 出版日期:2010-09-20 发布日期:2010-09-20
基金资助:
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).

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).

摘要/Abstract

摘要：

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.

关键词: Bloch constant, Bloch mapping, critical point, holomorphic mapping

Abstract:

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

中图分类号:

32H02

王建飞, 刘太顺, 唐笑敏. DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC Dⁿ[J]. 数学物理学报(英文版), 2010, 30(5): 1661-1668.

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

DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC Dⁿ

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