期刊文献+
共找到2篇文章
< 1 >
每页显示 20 50 100
Completely Invariant Domains of Holomorphic Self-Maps on C
1
作者 方丽萍 《Journal of Beijing Institute of Technology》 EI CAS 1997年第3期187-191,共5页
Let/(z) be a holomorph.self-map on C.-G-(0) with essential singularities 0 and It is proved that f(z) has a completdy invariant domain.D.F(f),then D is doubly connected and D contains all the singularities of the inv... Let/(z) be a holomorph.self-map on C.-G-(0) with essential singularities 0 and It is proved that f(z) has a completdy invariant domain.D.F(f),then D is doubly connected and D contains all the singularities of the inverse of f(z),moreover,if f is of the finite type, then D=F(f). This result implies that f(z) has at most one completely invariant domain in F(f). 展开更多
关键词 holomorphic maps completely invariant domains Fatou set
下载PDF
Nonexistence of Proper Holomorphic Maps Between Certain Classical Bounded Symmetric Domains 被引量:1
2
作者 Ngaiming MOK 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2008年第2期135-146,共12页
The author,motivated by his results on Hermitian metric rigidity,conjectured in [4] that a proper holomorphic mapping f:Ω→Ω′from an irreducible bounded symmetric domainΩof rank≥2 into a bounded symmetric domai... The author,motivated by his results on Hermitian metric rigidity,conjectured in [4] that a proper holomorphic mapping f:Ω→Ω′from an irreducible bounded symmetric domainΩof rank≥2 into a bounded symmetric domainΩ′is necessarily totally geodesic provided that r′:=rank(Ω′)≤rank(Ω):=r.The Conjecture was resolved in the affirmative by I.-H.Tsai [8].When the hypothesis r′≤r is removed,the structure of proper holomorphic maps f:Ω→Ω′is far from being understood,and the complexity in studying such maps depends very much on the difference r′-r,which is called the rank defect.The only known nontrivial non-equidimensional structure theorems on proper holomorphic maps are due to Z.-H.Tu [10],in which a rigidity theorem was proven for certain pairs of classical domains of type I,which implies nonexistence theorems for other pairs of such domains.For both results the rank defect is equal to 1,and a generaliza- tion of the rigidity result to cases of higher rank defects along the line of arguments of [10] has so far been inaccessible. In this article, the author produces nonexistence results for infinite series of pairs of (Ω→Ω′) of irreducible bounded symmetric domains of type I in which the rank defect is an arbitrarily prescribed positive integer. Such nonexistence results are obtained by exploiting the geometry of characteristic symmetric subspaces as introduced by N. Mok and L-H Tsai [6] and more generally invariantly geodesic subspaces as formalized in [8]. Our nonexistence results motivate the formulation of questions on proper holomorphic maps in the non-equirank case. 展开更多
关键词 Proper holomorphic maps Bounded symmetric domains Characteristic symmetric subspaces Invariantly geodesic subspaces Rank defects
原文传递
上一页 1 下一页 到第
使用帮助 返回顶部