$(m,d)$-内射盖与Gorenstein $(m,d)$-平坦模

研究了$(m,d)$-内射$R$-模作成的类是(预)盖类的条件,证明了$(m,d)$-凝聚环上的每一个左$R$-模都具有$(m,d)$-内射盖.在此基础上,又引入研究了Gorenstein $(m,d)$-平坦模和Gorenstein $(m,d)$-内射模,证明了$(m,d)$-凝聚环上的左$R$-模$M$是Gorenstein$(m,d)$-平坦模的充分必要条件是它的特征模$M^{+}$是Gorenstein $(m,d)$-内射模.推广了Goresntein平坦模和Goresntein $n$-平坦模上的一些结果.     

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。     

Proper holomorphic self-maps of smooth bounded Reinhardt domains in C~2

It is proved that every proper holomorphic self-map of a smooth bounded Reinhardt domain in C~2 is an automorphism.     

Proper holomorphic self-maps of smooth bounded Reinhardt domains in ?2

It is proved that every proper holomorphic self-map of a smooth bounded Reinhardt domain in ℂ² is an automorphism. The first author’s work was supported in part by the National Natural Science Foundation of China (Grant No. 10571135) and the Doctoral Program Foundation of the Ministry of Education of China (Grant No. 20050240711)     

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.     

Rigidity of Proper Self-Mapping on Some Kinds of Generalized Hartogs Triangle

It is proved that every proper holomorphic self-mapping of some kinds of Generalized Hartogs Triangles is an automorphism, and its explicit expression is given. Received March 1, 2001, Accepted August 24, 2001     

某些类型广义Hartogs三角型的逆紧自映射的刚性

本文证明某些类型广义Hartogs三角形的逆紧全纯自映射一定是自同构,同时给出这些自同构的明确表达式.     

CLASSIFICATION OF A CLASS OF HYPERBOLIC REINHARDT DOMAINS

In this article, the author discusses the dimension of holomorphic automorphism groups on hyperbolic Reirihardt domains. and classifies those hyperbolic Reinhardt domains whose automorphism group has prescribed dimension n2 - 2 (where n is the dimension of domain).     

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.     

The Bergman kernel function of some Reinhardt domains (Ⅱ)

The boundary behavior of the Bergman kernel function of a kind of Reinhardt domain is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points (Z,(Z-)). Let Ω be the Reinhardt domainm(X) where αj>0,j=1,2,…,n,N=N1+N2+…+Nn,‖Zj‖ is the standard Euclidean norm in CNj,j=1,2,…,n; and let K(Z,(W-)) be the Bergman kernel function of Ω. Then there exist two positive constants m and M,and a function F such that mF(Z,(Z-))≤K(Z,(Z-))≤MF(Z,(Z-))holds for every Z∈Ω. Here (X) and r(Z)=‖Z‖α-1 is the defining function of Ω. The constants m and M depend only on α=(α1,…,αn) and N1,N2,…,Nn,not on Z. This result extends some previous known results.     

一类Reinhardt域的群不变函数与不变Kahler度量

本文把［１］的结果推广到更广泛的一类Ｒｅｉｎｈａｒｄｔ域Ｄ＝Ｄ（ｋ１ｋ２…ｋｐ）　Ｃ（１≤ｐ＜ｎ），即利用Ｄ的解析自同构群Ａｕｔ（Ｄ）下不变函数给出了域Ｄ在Ａｕｔ（Ｄ）下不变的Ｋａｈｌｅｒ度量．     

Cn中F(p,q,s)型空间上的 Bergman型算子

设p0,s≥0,q+s-1,q+n-1.讨论了C~n中单位球上F(p,q,s)到本身或A(p,q,s)空间到L(p,q,s)空间上的Bergman型算子的有界性条件.