亚纯函数与其差分的唯一性

研究了亚纯函数与其差分算子分担多项式的唯一性问题,证明了:设f是一个有穷级非常数亚纯函数,p(z)(■0)是一个多项式.如果f,△_cf与△_c~2f CM分担∞,p(z),则f≡△_cf或f(z)=e~(Az+B)+b,其中p(z)≡b≠0,A≠0满足e~(Ac)=1.本文结果是对Chang, Fang(Chang J M, Fang M L. Uniqueness of entire functions and fixed points [J]. Kodai Math J, 2002, 25(1):309-320.)结果的差分模拟,并且完整回答了Chen, Chen(Chen B Q, Chen Z X, Li S. Uniqueness theorems on entire functions and their difference operators or shifts [J]. Abstr Appl Anal, 2012,Art. ID 906893, 8 pp.)的问题.     

涉及移动目标的亚纯映射唯一性定理

本文首先证明了一个新的从C~n到P~N(C)的亚纯映射第二基本定理,其中涉及到带有不同权重的截断型计算函数;其次利用这个新的第二基本定理,考虑了退化的亚纯映射在分担处于一般位置的移动超平面下的唯一性问题,并在较弱的条件下获得了一个唯一性结果,改进了已有的一些经典结果.     

一类线性差分方程的亚纯解与一个亚纯函数分担3个值的唯一性

主要研究差分方程a_1(z)f(x+1)+a_0(z)f(z)=F(z)的一个有穷级超越亚纯解f(z)与亚纯函数g(z)分担0,1,∞CM时的唯一性问题(其中a_(z),a0(z),F(z)为非零多项式,且满足a_1(z)+a_0(z)■0),得到f(x)≡g(z),或f(z)+g(z)≡f(z)g(z),或存在一个多项式β(z)=az+b_0和一个常数a_0满足e~(a_0)≠e~(b_0),使得f(z)=(1-e~(β(x)))/(e~(β(x))(e~(a_o-b_0)-1))与g(z)=(1-e~(β(x)))/(1-e~(b_o-a_0)),其中a(≠0),b_0为常数.     

亚纯映射的唯一性定理

证明了若干个亚纯映射的唯一性定理．     

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.     

涉及小映射的亚纯映射唯一性问题

得到了涉及3n+1个活动小函数的亚纯映射唯一性结果,改进了Fujimoto(1975)和Tu(2002)的定理.     

Borel方向与涉及重值的亚纯函数的唯一性

利用角域Nevanlinna特征函数和亚纯函数的辐角分布理论研究了亚纯函数的角域唯一性问题,获得了一些涉及重值的角域唯一性的结果,该角域包含亚纯函数的一条Borel方向.     

C~n中k次对称准凸映射在单位多圆柱某方向上的偏差定理(英文)

<正>We obtain a distortion theorem of Jacobian matrix Jf(z) for k-fold symmetric quasi-convex / along a unit direction in C~n on the unit polydisc.     

涉及较少小映射的多复变亚纯映射唯一性定理

证明了从C~m到P~n(C)的亚纯映射分担较少个数小映射的唯一性定理,改进和推广了最近的一些工作.     

涉及截断重数的亚纯映射的唯一性问题

研究了一个涉及截断重数的亚纯映射的唯一性问题,改进了陈志华和颜启明在2010年给出的一个结果.     

Uniqueness Theorem of Meromorphic Mappings with Moving Targets

Some uniqueness theorems of meromorphic mappings with moving targets are given under the inclusion relations between the zeros sets of meromorphic mappings.     

Second Main Theorem for Meromorphic Maps into Algebraic Varieties Intersecting Moving Hypersurfaces Targets*

Since the great work on holomorphic curves into algebraic varieties intersecting hypersurfaces in general position established by Ru in 2009, recently there has been some developments on the second main theorem into algebraic varieties intersecting moving hypersurfaces targets. The main purpose of this paper is to give some interesting improvements of Ru’s second main theorem for moving hypersurfaces targets located in subgeneral position with index.     

A Regularity Result for CR Mappings Between Infinite Type Hypersurfaces

The Schwarz reflection principle in one complex variable can be stated as follows. Let M and M′ be two real analytic curves in ? and f a holomorphic function defined on one side of M, extending continuously through M, and mapping M into M′. Then f has a holomorphic extension across M. In this paper, we extend this classical theorem to higher complex dimensions for a class of hypersurfaces of infinite type.     

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.     

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.     

The Defect Relation for Slowly Moving Target Hypersurfaces

Under certain assumptions, we extend the Carlson-Griffiths-King theory to prove a second main theorem for moving target hypersurfaces. This allows us to obtain the desired defect relation $$ sumlimits_{j = 1}^q {delta (f , g_j )} le {{n + 1} over p} $$     

Minimal Hypersurfaces in Hyperbolic Spaces

In this paper, we reprove a theorem of M. Anderson [Invent. Math., 69 （1982）, pp. 477-494] which established the existence of a minimal hypersurface in the hyperbolic space with prescribed asymptotic boundary with non-negative mean curvature in the non-parametric case. We use the mean curvature flow method.     

Growth Theorem and Distortion Theorem for a Sub class of Parab olic Starlike Mappings

In this article, we firstly introduce a subclass of parabolic starlike mappings writen as P S (β;ρ). Secondly, the growth theorem for P S (β;ρ) on the unit ball in complex Banach space is obtained. Finaly, as the application of the growth theorem of P S (β;ρ), the distortion theorem along a unit direction is also established.     

一类多复变全纯映照子族的增长和偏差定理

在一般复Banach空间X中的单位球B上引入一类全纯映照族M_g.考虑B上满足条件(Df(x))~(-1)f(x)∈M_g的正规化局部双全纯映照f(x)(其中x=0是f(x)-x的k+1阶零点)并得到其增长定理.作为应用,也得到了C~n中单位多圆柱D~n上映照f关于Jacobi矩阵Jf(z)的偏差定理,该结果统一和推广了星形映照许多子族的相应结论.