On Meromorphically Normal Families of Meromorphic Mappings of Several Complex Variables into P(C)

We shall prove some meromorphic normality criteria for families of meromorphic mappings of several complex variables into P^N(C), the complex N-dimensional projective space, related to Nochka's Picard type theorems. Some related results (e.g., extension theorems, improved normality criteria, and quasi-normality criteria) will be obtained also. The technique in this paper mainly depends on Stoll's normality criteria for families of non-negative divisors on a domain of Cⁿ.     

Normal families of meromorphic mappings of several complex variables into P~N(C) for moving targets

Motivated by Ru and Stoll's accomplishment of the second main theorem in higher dimension with moving targets, many authors studied the moving target problems in value distribution theory and related topics. But thereafter up to the present, all of researches about normality criteria for families of meromorphic mappings of several complex variables into PN(C) have been still restricted to the hyperplane case. In this paper, we prove some normality criteria for families of meromorphic mappings of several complex variables into PN(C) for moving hyperplanes, related to Nochka's Picard-type theorems. The new normality criteria greatly extend earlier related results.     

涉及复代数超曲面的全纯映射正规族

本文研究了涉及固定超曲面的全纯映照的正规性问题。利用Aladro 和Krantz对全纯映射族正规性的刻画和Shirosahi建立的一系列涉及一些特殊复代数超曲面的Picard 型定理,得到了全纯映射族的一些正规定则。     

Uniqueness Theorems for Meromorphic Mappings in Several Complex Variables into PN(C) with Two Families of Moving Targets

The authors prove some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space PN(C) with two families of moving targets, and the results obtained improve some earlier work.     

UNIQUENESS PROBLEM FOR MEROMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES INTO P^N（C） WITH TRUNCATED MULTIPLICITIES

This paper proves some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space P N(C) with truncated multiplicities,and our results improve some earlier work.     

Montel-Type Theorems in Several Complex Variables with Continuously Moving Targets

The authors introduce a new idea related to Montel-type theorems in higher dimension and prove some Montel-type criteria for normal families of holomorphic mappings and normal holomorphic mappings of several complex variables into p^N （C） for continuously moving hyperplanes in pointwise general position. The main results are also true for continuously moving hypersurfaces in pointwise general position. Examples are given to show the sharpness of the results.     

Normality criteria for families of holomorphic mappings of several complex variables into

By applying the heuristic principle in several complex variables obtained by Aladro and Krantz, we shall prove some normality criteria for families of holomorphic mappings of several complex variables into , the complex N-dimensional projective space, related to Green's and Nochka's Picard type theorems. The equivalence of normality to being uniformly Montel at a point will be obtained. Some examples will be given to complement our theory in this paper.

     

NORMAL CRITERION FOR FAMILIES OF HOLOMORPHIC MAPS OF SEVERAL COMPLEX VARIABLES INTO P~N(C)WITH MOVING HYPERSURFACES

This article gives a normal criterion for families of holomorphic mappings of several complex variables into P N(C)for moving hypersurfaces in pointwise general position,related to an Eremenko’s theorem.     

多复变Pang-Zalcman引理及应用

单复变中的Pang-Zalcman引理是研究亚纯函数正规族问题的重要工具.本文将该引理推广至多复变全纯函数的情形.作为应用建立了多复变全纯函数族的正规定则，改进和推广了相关结果.     

Results on Uniqueness Problem for Meromorphic Mappings Sharing Moving Hyperplanes in General Position Under More General and Weak Conditions

The aim of the paper is to deal with the algebraic dependence and uniqueness problem for meromorphic mappings by using the new second main theorem with different weights involved the truncated counting functions, and some interesting uniqueness results are obtained under more general and weak conditions where the moving hyperplanes in general position are partly shared by mappings from Cⁿ into P^N(C), which can be seen as the improvements of previous well-known results.     

亚纯函数族的几个正规定则

研究了亚纯函数族的正规族问题.利用Zalcman引理的方法,获得了亚纯函数族的几个正规定则.并改进了相关文献的结论.     

A degeneracy theorem for meromorphic mappings with truncated multiplicities

In this article, we prove a degeneracy theorem for three linearly non-degenerate meromorphic mappings from C n into P N (C), sharing 2N + 2 hyperplanes in general position, counted with multiplicities truncated by 2.     

涉及零点重数的亚纯函数的值分布

本文研究涉及零点重数的亚纯函数的值分布，证明了几个一般的模分布定理及相应的亚纯函数族的正规定则．     

截断型亚纯映射的唯一性定理涉及到小映射的情形

唯一性定理是多复变值分布中重要的定理之一,本文在已有的研究成果上,运用Thai最新得到的第二基本定理,给出了多复变中截断型亚纯映射新的唯一性定理涉及到小映射情形.     

Algebraic dependences of meromorphic mappings in several complex variables

We give some theorems on algebraic dependence of meromorphic mappings in several complex variables into complex projective spaces.     

Normal family of quasimeromorphic mappings

The more general quasimeromorphic mappings are studied with the geometric method. The necessary and sufficient conditions for the normality of the family of quasimeromorphic mappings are discussed. We proved two inequalities on the covering surface and obtained some normal criteria on quasimeromorphic mappings with them. Obviously, these criteria hold for meromorphic functions.     

关于亚纯函数的正规族

在本文研究了亚纯函数族的正规族问题,利用Zalcman引理的方法,获得了亚纯函数族的几个正规定则.并改进了顾永兴和Bergweiler的结果.     

Uniqueness problem for meromorphic mappings in several complex variables with few hyperplanes

The purpose of this article is to deal with uniqueness problem with truncated multiplicities for meromorphic mappings in several complex variables. We obtain a degeneracy theorem of meromorphic mappings without taking account of multiplicities of order k in counting functions and a uniqueness theorem for meromorphic mappings sharing 2n + 2(n ≥ 2) hyperplanes in general position, which improve and extend some earlier work.     

Picard values and normal families of meromorphic functions with multiple zeros

In this paper, general modular theorems are obtained for meromorphic functions and their derivatives. The related criteria for normality of families of meromorphic functions are proved. Research supported by the National Science Foundation of China     

一类亚纯函数的正规定则

该文研究了一类亚纯函数的一般性的正规定则.其结果推广了以前与之相关的一系列结果.