复Banach空间单位球上准凸映射的增长定理与掩盖定理

在一般复Banach空间中的单位球上讨论了一类严格介于凸映射类与星形映射类的"准凸映射类”, 证明了准凸映射具有与凸映射类完全相同的增长定理与掩盖定理. 同时证明了它与K. A. Roper和T. J. Suffridge在 中单位球上所定义的"A型准凸映射类"完全一致.     

复Banach空间中单位球上双全纯凸映射的偏差定理

本文讨论一般复Banach空间上单位球B的Caratheodory度量和Kobayashi 度量的性质,并据此将Cn(n≥1)中单位球Bn上双全纯凸映射的矩阵形式偏差定理 推广到一般复Banach空间的单位球B上.     

多复变数星形映射在某方向上精确的偏差定理

研究了Cn中单位多圆柱上星形映射在某方向上精确的偏差定理．给出了复Banach空间单位球的某方向上精确的偏差的上界,同时给出了下界的猜测．     

单位球上α次准凸映射精细的偏差定理

利用欧氏空间单位球的边界型Schwarz引理给出α次准凸映射在极值点处精细的行列式型偏差定理和矩阵型偏差定理.     

多复变数完全拟凸映射的分解定理

设Ω1(∪) Cn1,Ω2(∪)Cn2为凸的Reinhardt域,f(z,w)=(f1(z,w),f2(z,w))′为Ω1×Ω2上的正规化全纯映射.本文证明f为Ω1×Ω2上的正规化双全纯完全拟凸映射当且仅当f(z,w)=(Φ1(z),Φ2(W))′,其中ΦjΩj→Cnj是Ωj(j=1,2)上的正规化双全纯完全拟凸映射.     

多复变数完全拟凸映射的分解定理

设Ω_1C~(n1),Ω_2C~(n2)为凸的Reinhardt域,f(z,w)=(f1(z,w),f2(z,w))'为Ω_1×Ω_2上的正规化全纯映射.本文证明f为Ω_1×Ω_2上的正规化双全纯完全拟凸映射当且仅当 f(z,w)=(Φ_1(z),Φ_2(w))'其中φj:Ωj→C~(nj)是Ωj(j=1,2)上的正规化双全纯完全拟凸映射。     

多圆柱上的完全准凸映射

在C~n中有界凸Reinhardt域上讨论了一类介于凸映射类与星形映射类之间的“完全准凸映射类”.特别地,在C~n中的多圆柱上给出了完全准凸映射的分解定理,得到了多圆柱上判别凸映射的一个改进的充分条件.     

多圆柱上的完全准凸映射

在Cn中有界凸Reinhardt域上讨论了一类介于凸映射类与星形映射类之间的"完全准凸映射类".特别地,在Cn中的多圆柱上给出了完全准凸映射的分解定理,得到了多圆柱上判别凸映射的一个改进的充分条件.     

~n中双全纯凸映射的偏差定理

本文通过考虑n（n≥1）中单位球Bn上双全纯凸映射展开式的二阶系数估计,研究了该类映射的一种偏差定理,推广并改进了龚升等人（见[1]）的工作。     

一类Reinhardt域上正规化双全纯完全准凸映射的分解定理

文主要研究Cⁿ 中一类有界凸的Reinhardt 域D_M上正规化双全纯完全准凸映射的齐次展式问题. 建立了D_M上完全准凸映射的分解定理, 并对D_M上星形映射进行一些探讨.     

一类多复变全纯映照子族的增长和偏差定理

在一般复Banach空间X中的单位球B上引入一类全纯映照族M_g.考虑B上满足条件(Df(x))~(-1)f(x)∈M_g的正规化局部双全纯映照f(x)(其中x=0是f(x)-x的k+1阶零点)并得到其增长定理.作为应用,也得到了C~n中单位多圆柱D~n上映照f关于Jacobi矩阵Jf(z)的偏差定理,该结果统一和推广了星形映照许多子族的相应结论.     

On Spirallike Mappings in Several Complex Variables

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ１９３３,Ｈ．ｃａｒｔａｎｐｏｉｎｔｅｄｏｕｔｔｈａｔｔｈｅｒｅｄｏｅｓｎｏｔｅｘｉｓｔｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇＢｉｅｂｅｒｂａｃｈｃｏｎ－ｊｅｃｔｕｒｅｆｏｒｂｉｈｏｌｏｍｏｒｐｈｉｃｍａｐｐｉｎｇｓｉｎｓｅｖｅｒａｌｃｏｍｐｌｅｘｖａｒｉａｂｌｅｓ．Ｈｅａｌｓｏｐｏｉｎｔｅｄｏｕｔｔｈｅｃｏｒｒｅ－ｓｐｏｎｄｉｎｇｇｒｏｗｔｈａｎｄｃｏｖｅｒｉｎｇｔｈｅｏｒｅｍｓｆａｉｌｉｎｔｈｅｃａｓｅｏｆｓｅｖｅｒａｌｃｏｍｐｌｅｘｖａｒｉａｂｌｅｓ．Ｔｈｅｎ…     

多复变数的抛物星形映射

本文给出了抛物星形映射,ρ次的抛物星形映射,抛物形β型螺形映射和ρ次的抛物形β型螺形映射的定义.证明了推广的Rope-Suffridge算子保持这些映射的几何性质不变.     

Degeneracy and Finiteness Theorems for Meromorphic Mappings in Several Complex Variables

The author proves that there are at most two meromorphic mappings of C~m into P~n(C)(n ≥ 2) sharing 2 n+ 2 hyperplanes in general position regardless of multiplicity,where all zeros with multiplicities more than certain values do not need to be counted. He also shows that if three meromorphic mappings f~1, f~2, f~3 of Cminto P~n(C)(n ≥ 5) share2 n+1 hyperplanes in general position with truncated multiplicity, then the map f~1×f~2×f~3 is linearly degenerate.     

Sharp Growth Theorems and Coefficient Bounds for Starlike Mappings in Several Complex Variables

Let B be the unit ball in a complex Banach space. Let S^＊k＋1（B） be the family of normalized starlike mappings f on B such that z = 0 is a zero of order k ＋ 1 of f（z） - z. The authors obtain sharp growth and covering theorems, as well as sharp coefficient bounds for various subsets of S^＊k＋1（B）.     

多复变数的双全纯映照

本文对复变数几何函数论的结果向多复变函数的推广进行了系统的研究，是作者及其合作者们在此项研究工作上的一些成果的综合报导。此文集中讨论了有界对称域及Ｒｅｉｎｈａｒｄｔ域的情形，讨论了全纯映照为星形、凸及双全纯的种种条件，建立了一些双全纯映照族的偏差定理，增长定理及掩盖定理，定义了高维空间上的Ｓｃｈｗａｒｔｚ导数。对有界对称域上的全纯凸函数的Ｂｌｏｃｈ常数进行了估计，处理这些问题的主要工具之一为李代数     

The Coefficient Inequalities for a Class of Holomorphic Mappings in Several Complex Variable

The authors establish the coefficient inequalities for a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in ■ⁿ,which are natural extensions to higher dimensions of some Fekete and Szeg? inequalities for subclasses of the normalized univalent functions in the unit disk.     

Mappings Which Have a Parametric Representation in Several Complex Variables

In this paper, the sharp distortion theorems of the Fr\''echet-derivative type for a subclass of biholomorphic mappings which have a parametric representation on the unit ball of complex Banach spaces are established, and the corresponding results of the above generalized mappings on the unit polydisk in $\mathbb{C}^n$ are also given. Meanwhile, the sharp distortion theorems of the Jacobi determinant type for a subclass of biholomorphic mappings which have a parametric representation on the unit ball with an arbitrary norm in $\mathbb{C}^n$ are obtained, and the corresponding results of the above generalized mappings on the unit polydisk in $\mathbb{C}^n$ are got as well. Thus, some known results in prior literatures are generalized.     

Montel-Type Theorems in Several Complex Variables with Continuously Moving Targets

The authors introduce a new idea related to Montel-type theorems in higher dimension and prove some Montel-type criteria for normal families of holomorphic mappings and normal holomorphic mappings of several complex variables into p^N （C） for continuously moving hyperplanes in pointwise general position. The main results are also true for continuously moving hypersurfaces in pointwise general position. Examples are given to show the sharpness of the results.