| Bloch Constant of Holomorphic Mappings on the Unit Ball of C~n |
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| 引用本文： | Jianfei WANG~* Taishun LIU~(**) *Department of Mathematics,University of Science and Technology of China,Hefei 230026,China. **Department of Mathematics,Huzhou Teachers College,Huzhou 313000,Zhejiang,China.. Bloch Constant of Holomorphic Mappings on the Unit Ball of C~n[J]. 数学年刊B辑(英文版), 2007, 0(6) |
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| 作者姓名： | Jianfei WANG~* Taishun LIU~(**) *Department of Mathematics University of Science and Technology of China Hefei 230026 China. **Department of Mathematics Huzhou Teachers College Huzhou 313000 Zhejiang China. |
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| 基金项目： | Project supported by the National Natural Science Foundation of China(No.10571164)，Specialized Research Fund for the Doctoral Program of Higher Education(No.20050358052)，the Zhejiang Provincial Natural Science Foundation of China(No.Y606197). |
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| 摘 要： | In this paper,the authors establish distortion theorems for various subfamilies H_k(B)of holomorphic mappings defined in the unit ball in C~n with critical points,where k is any positive integer.In particular,the distortion theorem for locally biholomorphic mappings is obtained when k tends to ∞.These distortion theorems give lower bounds on|det f′(z)|and Re det f′(z).As an application of these distortion theorems,the authors give lower and upper bounds of Bloch constants for the subfamiliesβ_k(M)of holomorphic mappings.Moreover,these distortion theorems are sharp.When B is the unit disk in C,these theorems reduce to the results of Liu and Minda.A new distortion result of Re det f′(z)for locally biholomorphie mappings is also obtained.
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Bloch Constant of Holomorphic Mappings on the Unit Ball of C~n |
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| Jianfei WANG Taishun LIU. Bloch Constant of Holomorphic Mappings on the Unit Ball of C~n[J]. Chinese Annals of Mathematics,Series B, 2007, 0(6) |
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| Authors: | Jianfei WANG Taishun LIU |
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| Abstract: | |
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| Keywords: | Bloch constant Holomorphic mappings Locally biholomorphic mappings Critical points |
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