Proper Holomorphic Mappings Between n-generalized Hartogs Triangles

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...     

The Classification of Proper Holomorphic Mappings Between Special Hartogs Triangles of Different Dimensions

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

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…     

不等维广义Hartogs三角形之间的逆紧全纯映射

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.     

C2中某类Hartogs域的逆紧全纯自映射

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.     

C~2中某类Hartogs域的逆紧全纯自映射

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．     

全纯逆紧映射的全纯延拓性和广义Hartogs三角形上的全纯逆紧映射

对满足一定条件的非光滑有界域上的全纯逆紧映射证得了局部全纯延拓定理. 同时也研究了广义Hartogs三角形之间的全纯逆紧映射.     

The Degree of Proper Holomorphic MappingsBetween Special Domains in C^n

Let Gi be closed Lie groups of U (n), Ω i be bounded Gi-invariant domains in C^n which contains 0, and O(C^n)^Gi = C, for i = 1, 2. It is known that if f : Ω 1 → Ω 2 is a proper holomorphic mapping, and f^-1{0} = {0}, then f is a polynomial mapping. In this paper, we provide an upper bound for the degree of such a polynomial mapping using the multiplicity of f .     

Proper Holomorphic Self-Maps of Quasi-balanced Domains

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.     

Biholomorphic Mappings and the Extension Operators on New Hartogs Domains

In this paper, we generalize the Roper–Suffridge operator on the extended Hartogs domains.By using the geometric properties and the growth theorems of subclasses of biholomorphic mappings,we obtain the generalized operators preserve the properties of parabolic and spirallike mappings of type β and order ρ, S*_Ω(β, A, B), almost starlike mapping of complex order λ on ΩN under different conditions, and thus we get the corresponding results on the unit ball B~n in C~n. The conclusions lead to some known results.     

有界星形圆型域上的零伦全纯映照

星形映照与螺形映照是多复变函数论中两个重要的映照类,他们共同的几何特征是其像域中任一点到原点的直线或螺线完全落在该像域中.利用拓扑学知识,从同伦的观点出发研究具有上述几何特征的映照,并得出其上的零伦全纯映照的判别方法,所得结论对复欧式空间Cⁿ中的单位球Bn中的单位球Bⁿ同样成立.     

Properties of New Holomorphic Mappings with Respect to Conic Domains

This paper is mainly about holomorphic mappings associated with conic regions which are closely connected with k-ST(α). We introduce new subclasses of starlike(spirallike) functions,namely, S_c~p(k, α)(S_c~p(k, α, β)), and discuss their coefficient estimates and the Fekete–Szeg?–Goluzin's problem. Then we generalize S_c~p(k, α, β) on the unit ball B~n in C~n, that is, k-conic spirallike mappings of type β and order α. We obtain the growth, covering and distortion theorems of the generalized mappings. Besides that, we construct k-conic spirallike mappings of type β and order α on B~n through S_c(k, α, β) by the generalized Roper-Suffridge extension operators.     

Nonexistence of Proper Holomorphic Maps Between Certain Classical Bounded Symmetric Domains

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.     

关于典型域到单位球上全纯映射的注记

给出了从典型域到单位球的全纯映射高阶Frchet导数的Schwarz-Pick估计,从而推广了单位球上全纯自映射Frchet导数的Schwarz-Pick估计以及单位圆盘上有界全纯函数高阶导数的Schwarz-Pick估计的结论.     

Proper Holomorphic Maps from Domains in C2 with Transverse Circle Action

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.     

Classification of Recurrent Domains for Holomorphic Maps on Complex Projective Spaces

We generalize the classification of recurrent domains for holomorphic maps on two-dimensional complex projective space given in Fornæss and Sibony (Math. Ann. 301:813–820, 1995) to higher dimensions. In particular, we show that an invariant recurrent Fatou component is either an attracting basin or a Siegel domain or it retracts to a lower-dimensional Siegel manifold.     

双全纯映照的一些偏微分不等式

该文在有界星形圆型域上建立一些与双全纯星形映照有关的偏微分不等式．作为应用，给出有界星形圆型域上ε星形映照以及近似星形映照的一些充分判别条件．     

Compact Sets of Holomorphic Mappings

Compactness of locally bounded sets of holomorphic functions with infinite dimensional domains is connected, using Heinrich's density condition, to the Schwartz and semi-Montel properties on the domain. The metrizability of bounded subsets for various spaces of holomorphic functions is investigated.     

L p,q -Boundedness of Bergman Projections in Homogeneous Siegel Domains of Type II

In this paper, we generalize to homogeneous Siegel domains of second kind the L ^p -continuity properties of the Bergman projection. Precisely, we give an improvement of the index p using Fourier analysis as in the case of convex homogeneous tube type domains (Nana and Trojan in Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) X:477–511, 2011).