In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not pre...In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.展开更多
In this paper, the authors establish distortion theorems for various subfamilies Hk（B） of holomorphic mappings defined in the unit ball in C^n with critical points, where k is any positive integer. In particular, th...In this paper, the authors establish distortion theorems for various subfamilies Hk（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 subfamilies βk（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 biholomorphic mappings is also obtained.展开更多
文摘In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.
基金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).
文摘In this paper, the authors establish distortion theorems for various subfamilies Hk（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 subfamilies βk（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 biholomorphic mappings is also obtained.
