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Distortion theorems on the Lie ball RIV(n) in Cn
wangjianfei 1 * #,Liu Taishun 2,Xu Huiming 1
1.zhejiang normal university
2.department of mathematic, huzhou teachers college
*Correspondence author
#Submitted by
Subject:
Funding: 国家自然科学基金,教育部博士点基金,浙江省自然科学基金（No.10571164; 20050358052; Y606197）
Opened online:12 January 2009
Accepted by: none
Citation: wangjianfei,Liu Taishun,Xu Huiming.Distortion theorems on the Lie ball RIV(n) in Cn[OL]. [12 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27691
 
 
In this paper, we introduce the subfamilies Hm(RIV(n)) of holomorphic mappings defined on the Lie ball RIV(n) which take into consideration the m-order to which the Jacobian determinant must vanish, as well as for the limiting case of locally biholomorphic mappings. Various distortion theorems for holomophic mappings Hm(RIV(n)) are established. The distortion theorems coincide with Liu and Minda as the special case of the unit disk. When m = 1 and m ! +1, the distortion theoerems reduce to the results obtained by Gong for RIV(n), respectively. Moreover, our method is different. As an application, the bounds for Bloch constants of Hm(RIV(n)) are given.
Keywords:Distortion theorem;Bloch constant;Bloch mapping
 
 
 

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