Acta mathematica scientia, Series B >
DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC Dn
Received date: 2008-03-18
Revised date: 2008-11-19
Online 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).
In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc Dn with 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
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 . DOI: 10.1016/S0252-9602(10)60159-2
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