Reinhardt域B_p上正规化双全纯完全准凸映射的齐次展式

本文主要研究C~n中有界凸Reinhardt域B_p上正规化双全纯完全准凸映射的齐次展开式问题,设f(z):B_p→C~n(p＞2)是一个正规化双全纯完全准凸映射,k是满足k＜p≤k+1的自然数,那么f_j(z)=z_j+α_(j2)z_j~2+…+α_(jk)z_j~k+O(|z|~(K+1)),其中f_j是f的第j个分量,j=1,2…．,n．     

The Covering Theorems for Normalized Holomorphic Mappings on Bounded Starlike Circular Domains in C~n

In this paper, we will investigate convex domains and starlike domains which contain the image set of normalized holomorphic mappings on bounded starlike circular domains in Cn.     

锥伪单调和锥严格拟凸映射向量平衡问题

研究在锥伪单调、锥拟凸、锥严格拟凸和次连续条件下几类二元向量平衡问题解的关系，利用KyFan不动点定理证明了解的存在性。     

Proper Holomorphic Mappings Between Some Nonsmooth Domains

61. IntroductionLet DI, DZ be two bounded domains in C", a holomorphic mapping F: DI ~ DZ isproper if F--'(K) is compact whenever K is compact. It is Obvious that for every boUndeddomain in C", there always edests proper holomorphic self-mapping. However, given tabbounded domains DI, DZ in C", it does not seem easy to answer whether there ealsts properholomorphic mapping F: DI ~ D2. A main result obtained in recellt y6ars isTheorem 1.1.[1] Let Z (a) and Z (P) be two Generalized P…     

拟共形映射和弱Cigar域

设f是R~n到R~n上的同胚,本文证明了f是拟共形映射的充要条件是f将R~n中的任一弱Cigar域映成R~n中的弱Cigar域。     

高维空间中的有界凸域

证明n维空间中的有界凸域D能被拟共形映射到n维单位球B~n(0,1),即D是拟球,从而说明拟共形映射中的黎曼定理在n维空间中的有界凸域类中是成立的．     

B_p~n上双全纯凸映照

本文给出了Suffridge结果的简单证明,并且构造出Reinhardt域B_p~n上的一些双全纯凸映照     

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     

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.     

一类有界Reinhardt域上的函数论

In this paper, we consider a class of bounded Reinhardt domains Dα(m, n1,…,nm). The Bergman kernel function K(z,z), the Bergman metric matrix T(z,z), the Cauchy-Szego kernel function S(z,ζ) are obtained. Then we prove that the formal Poisson kernel function is not a Poisson kernel function. At last, we prove that Dαis a quasiconvex domain and Dαis a stronger quasiconvex domain if and only if Dαis a hypersphere.     

The generalized Roper-Suffridge extension operator on bounded complete Reinhardt domains

The generalized Roper-Suffridge extension operator Ф(f) on the bounded complete Reinhardt domain Ω in Cn with n ≥ 2 is defined by Φrn,β2,γ2,…,βn,γn(f)(z)=(rf(z1/r),(rf(z1/r)/z1)β2(f'(z1/r))γ2z2,…,(rf(z1/r)/z1)βn(f'(z1/r)γnzn) for (z1,z2,…,zn) ∈Ω, where r = r(Ω) = sup{|z1| (z1,z2,…,zn) ∈ Ω},0 ≤ γj ≤ 1 -βj,0 ≤ βj ≤ 1,and we choose the branch of the power functions such that (f(z1)/z1)βj |z1=0 = 1 and (f′(z1))γj |z1=0 =1,j = 2,…,n. In this paper, we prove that the operator Фrn,β2,γ2,…,βn,γn(f) is from the subset of S*α(U) to S*α(Ω)(0 ≤ α ＜ 1) on Ω and the operator Фrn,β2,γ2,…, βn,γn(f) preserves the starlikeness of order α or the spirallikeness of type β on Dp for some suitable constantsβj,γj,pj, where Dp ={(z1,z2,…,zn) ∈ Cn ∑nj=1|zj|pj ＜ 1} (pj ＞ 0, j = 1,2,…,n), U is the unit disc in the complex plane C, and Sα* (Ω) is the class of all normalized starlike mappings of order α on Ω. We also obtain that Φrn,β2,γ2,…,γn(f) ∈ S*α(Dp) if and only if f ∈ S*a(U) for 0 ≤ α ＜ 1 and some suitable constants βj,γj,pj.     

度量空间中拟对称映射与拟双曲一致域的研究

本文主要考虑度量空间中拟双曲一致域与拟对称映射之间的关系,并证明了度量空间中拟双曲一致域在拟对称映射下仍然是保持不变的.     

关于有界域的逆紧映照

本文对近20年来多复变函数的一个发展迅速的数学热门分支－逆紧映照作了一个回顾和整理。这是作者继续从事此方向研究的先声，也希望本文能为有志于此的研究者提供一些便利。本文从经典的结果开始，通过对逆紧映照在边界上的开拓及分支点的分布的讨论，详细地阐述了这些年来关于逆紧映照何时成为双全纯映照的若干结果。最后，对近年来关于逆紧映照另外的一些工作进行了简单的介绍。     

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。     

有界凸平衡域上的双全纯凸映照的判别准则

本文讨论Cn中有界强凸平衡域和凸平衡域上局部双全纯映照成为双全纯凸映照的充要条件,从而得到Reinhardt域Dp= 上双全纯凸映照的充要条件,其中Pj≥2(j=1,2,…,n).     

On Decomposition Theorem of normalized biholomorphic convex mappings in Reinhardt domains

The construction of normalized biholomorphic convex mappings in the Reinhardt domain Dp = of Cn is discussed. The authors set up a Decomposition Theorem for such mappings. As a special case, it is proved that, for each such mapping f, the first k-terms of the homogeneous expansion of its j-th component fj, j = 1, 2, ... ,n, depends only on zj, where k is the number that satisfies k 相似文献   

Convex mappings on some Reinhardt domains

In this paper, we consider the following Reinhardt domains. Let M = （M1, M2,..., Mn） ： [0,1] → [0,1]^n be a C2-function and Mj（0） = 0, Mj（1） = 1, Mj″ 〉 0, C1jr^pj-1 〈 Mj′（r） 〈 C2jr^pj-1, r∈ （0, 1）, pj 〉 2, 1 ≤ j ≤ n, 0 〈 C1j 〈 C2j be constants. Define
DM={z=（z1,z2,…,Zn）^T∈C^n：n∑j=1 Mj（｜zj｜）〈1}
Then DM C^n is a convex Reinhardt domain. We give an extension theorem for a normalized biholomorphic convex mapping f ： DM -→ C^n.     

A Class of Cone Bounded Quasiconvex Mappings in Topological Vector Spaces

Within the context of cone-ordered topological vector spaces, this paper introduces the concepts of cone bounded point and cone bounded set for vector set. With their aid, a class of new cone quasiconvex mappings in topological vector spaces is defined, and their fundamental properties are presented. The relationships between the cone bounded quasiconvex mapping defined in this paper and cone convex mapping, and other known cone quasiconvex mapping are also discussed.     

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.     

A Boundary Schwarz Lemma for Holomorphic Mappings on the Polydisc

The authors prove a general Schwarz lemma at the boundary for holomorphic mappings from the polydisc to the unit ball in any dimensions. For the special case of one complex variable, the obtained results give the classic boundary Schwarz lemma.