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1.
本文主要研究单位球B~n到单位球B~N上全纯逆紧映射的问题.对于B~n到B~N的全纯逆紧映射映射,当其几何秩为κ_0且N=n+((2n-κ_0-1)κ_0)/2时,给出了其正规化映射的一个刻画.  相似文献   

2.
韩静  陈志华 《数学年刊A辑》2006,27(1):119-128
本文对某类广义Hartogs三角形上的逆紧全纯自映射证明了刚性定理,即逆紧全纯自映射必定为全纯自同构.同时完全刻画了其全纯自同构群,并且给出了关于其全纯自同构以及两个这类域之间逆紧全纯映射的分类.  相似文献   

3.
一类广义Hartogs三角形之间逆紧映射的分类   总被引:1,自引:0,他引:1  
本文主要证明一类广义Hartogs三角形之间的逆紧全纯映射在相差全纯自同构的意义下是唯一的.  相似文献   

4.
本文对某类广义Hartogs三角形上的逆紧全纯自映射证明了刚性定理,即逆紧全纯自映射必定为全纯自同构.同时完全刻画了其全纯自同构群,并且给出了关于其全纯自同构以及两个这类域之间逆紧全纯映射的分类。  相似文献   

5.
本文主要证明一类广义Hartogs三角形之间的逆紧全纯映射在相差全纯自同构的意义下是唯一的。  相似文献   

6.
戴绍虞 《数学年刊A辑》2007,28(2):297-304
对C2中某类Hartogs域的逆紧全纯自映射证明了刚性定理,即逆紧全纯自映射必定为全纯自同构.此类域是光滑有界拟凸完全的Hartogs域,且它的边界上具有无限型点.  相似文献   

7.
对C2中某类Hartogs域的逆紧全纯自映射证明了刚性定理,即逆紧全纯自映射必定为全纯自同构.此类域是光滑有界拟凸完全的Hartogs域,且它的边界上具有无限型点.  相似文献   

8.
给出了不等维的蛋型域和广义Hartogs三角形之间的逆紧全纯映射存在的充要条件.  相似文献   

9.
单位圆盘的全纯自同构是《复变函数》课程中重要的内容之一,本文给出了单位圆盘的全纯自逆紧映照,其为单位圆盘的全纯自同构的一种推广,可供讲授《复变函数》课程的教师参考.  相似文献   

10.
本文首先回顾单位圆盘到复平面之间不存在逆紧全纯映照的证明,然后给出这一经典结果在高维情形下的推广,例如,在n维全纯可分离流形的一个相对紧域到Cn之间不存在逆紧全纯映照.本文还研究复空间的某些解析性质在逆紧全纯映照下保持不变,如双曲性、测度双曲性、有界全纯函数的存在性及有界多次调和函数的存在性等.  相似文献   

11.
We show that proper holomorphic self-maps of smoothly bounded pseudoconvex quasi-balanced domains of finite type are automorphisms. This generalizes the classical Alexander’s theorem on proper holomorphic self-maps of the unit ball.  相似文献   

12.
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…  相似文献   

13.
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.  相似文献   

14.
Rong  Feng  Zhang  Shuo 《数学学报(英文版)》2022,38(6):1002-1014
Acta Mathematica Sinica, English Series - In this paper, we first introduce the notion of n-generalized Hartogs triangles. Then, we characterize proper holomorphic mappings between some of these...  相似文献   

15.
The authors discuss the proper holomorphic mappings between special Hartogs triangles of different dimensions and obtain a corresponding classification theorem.  相似文献   

16.
We prove that a proper holomorphic map on the unit disk in thecomplex plane is uniquely determined up to post-compositionwith a Möbius transformation by its critical points. 1991Mathematics Subject Classification 30C99, 30F45.  相似文献   

17.
The authors consider proper holomorphic mappings between smoothly bounded pseudoconvex regions in complex 2-space,where the domain is of finite type and admits a transverse circle action.The main result is that the closure of each irreducible component of the branch locus of such a map intersects the boundary of the domain in the union of finitely many orbits of the group action.  相似文献   

18.
The authors consider proper holomorphic mappings between smoothly bounded pseudoconvex regions in complex 2-space, where the domain is of finite type and admits a transverse circle action. The main result is that the closure of each irreducible component of the branch locus of such a map intersects the boundary of the domain in the union of finitely many orbits of the group action.  相似文献   

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