Algebraic values of meromorphic functions on Riemann surfaces

We extend the Schneider-Lang theorem concerning algebraic values of meromorphic functions on the complex plane to meromorphic functions on punctured Riemann surfaces by using Jensen's formula for Riemann surfaces.     

Some radii problems related to certain p-valent meromorphic functions

The purpose of the present paper is to introduce several new classes of p-valent meromorphic functions defined by Ruscheweyh derivative operator for meromorphic multivalent functions. Further, we investigate the radii problems of these analytic classes in the punctured unit disk.     

SANDWICH-TYPE THEOREMS FOR MEROMORPHIC MULTIVALENT FUNCTIONS ASSOCIATED WITH THE LIU-SRIVASTAVA OPERATOR＊

The purpose of this article is to obtain some subordination and superordination preserving properties of meromorphic multivalent functions in the punctured open unit disk associated with the Liu-Srivas...     

On the Meromorphic Functions in the Punctured Plane Without Multiple Values

The study of meromorphic functions without multiple values in the plane started by F. Nevanlinna is extended to meromorphic functions in the punctured plane \({\mathbb {C}}^{{*}}.\) It is a classical result that a meromorphic function \(f\left( z\right) \) can be obtained as quotient of solutions of the second order differential equation \(u^{{\prime \prime }}+\left\{ f\left( z\right) ,z\right\} u=0,\) where \(\left\{ f\left( z\right) ,z\right\} \) is the Schwarzian derivative of \(f\left( z\right) \). In our hypothesis of meromorphic functions of finite order without multiple values in the puntured plane, the Schwarzian derivative \(\left\{ f\left( z\right) , z\right\} \) turns out to be a rational function with only possible poles at 0 and \(\infty \). In these conditions the asymptotic behaviour of \(f\left( z\right) \) can be described by a result of Hille (Lectures on Ordinary Differential Equations in the complex plane, Addison Wesley, Boston, 1969) on ordinary differential equations in the complex plane. The results obtained are framed in the value distribution theory of meromorphic functions, in particular in the punctured plane we shall consider the work of Khrystiyanin and Kondratyuk (Mat Stud 23(1):19–30, 2005; Mat Stud 23(1):57–68, 2005) and Korhonen (Nevanlinna theory on an annulus. Value distribution theory and related topics. Adv. Complex analysis and applications, Kluwer Academic Publishers, Dordrecht, 2004).     

Convolution properties of some classes of meromorphic univalent functions

Convolution technique and subordination theorem are used to study certain class of meromorphic univalent functions in the punctured unit disc.     

On a certain classes of meromorphic functions with positive coefficients

In this paper certain classes of meromorphic functions in punctured unit disk are defined. Some properties including coefficient inequalities, convolution and other results are investigated.     

Subordination properties for meromorphic multivalent functions associated with the multiplier transformation

The purpose of the present paper is to obtain some sandwich-type theorems, which are combined by subordination and superordination preserving properties associated with a certain family of multiplier transformations for meromorphic multivalent functions in the punctured open unit disk.     

Some convolution conditions for starlikeness and convexity of meromorphically multivalent functions

By making use of the Hadamard product (or convolution), the authors derive necessary and sufficient conditions for a suitably normalized meromorphically p-valent function to be in the familiar classes of meromorphic p-valently starlike and meromorphic p-valently convex functions in the punctured unit disk.     

Minimal surfaces in R3 with one end¶and bounded curvature

We study complete minimal surfaces M immersed in R ³, with finite topology and one end. We give conditions which oblige M to be conformally a compact Riemann surface punctured in one point, and we show that M can be parametrized by meromorphic data on this compact Riemann surface. The goal is to prove that when M is also embedded, then the end of M is asymptotic to an end of a helicoid (or M is a plane). Received: 13 January 1997 / Revised version: 15 September 1997     

无穷远点处亚纯单叶函数的拟Hadamard卷积(英文)

本文研究了圆环域U内亚纯星象和凸象函数的某些新子类的拟Hadamard卷积.利用卷积方法,获得了该类函数的与拟Hadamard卷积有关的某些性质,推广了一些已知结果.     

Extremal problems for quasiconformal maps of punctured plane domains

The main goal of this paper is to give an affirmative answer to the long-standing conjecture which asserts that the affine map is a uniquely extremal quasiconformal map in the Teichmüller space of the complex plane punctured at the integer lattice points. In addition we derive a corollary related to the geometry of the corresponding Teichmüller space. Besides that we consider the classical dual extremal problem which naturally arises in the tangent space of the Teichmüller space. In particular we prove the uniqueness of Hahn-Banach extension of the associated linear functional given on the Bergman space of the integer lattice domain. Several useful estimates related to the local and global properties of integrable meromorphic functions and the delta functional (see the definition below) are also obtained. These estimates are intended to study the behavior of integrable functions near singularities and they are valid in general settings.

     

无穷级拟亚纯映射的充满圆及Borel方向

对于平面上的K-拟亚纯映射，文献^[1]里证明了有限正级K-拟亚纯映射必定存在充满圆序列及Borel方向；本文进一步证明了对于平面上无穷级K-拟亚纯映射也存在充满圆序列及Borel方向．     

Nevanlinna theory of meromorphic functions on annuli

In this survey paper, we discuss the recent development of Nevanlinna theory of meromorphic functions on annuli, which extends results in Nevanlinna theory in the complex plane or in a disk. In particular, we show that the approach taken on annuli is a unified treatment of functions meromorphic in the complex plane, a disk and an annulus. It allows one to obtain many results in the complex plane and in a disk as corollaries of our results in annuli.     

关于亚纯函数的ρ(r)相对亏量

该文定义并研究ρ(0<ρ<+∞)级亚纯函数的ρ(r)相对亏量,得到了四个结果,其中定理2包含了Sarangi和Patil的结果,定理4表明具有极值ρ(r)亏量和的亚纯函数不再有非零有穷ρ(r) 相对亏值.     

拟亚纯映射的Borel方向

对于平面上的Ｋ－拟亚纯映射时,建立了一个角域的基本不等式,由此证明了Ｋ－拟亚纯映射的Ｂｏｒｅｌ方向的存在性及其相应性质。     

亚纯函数及其导数在角域内的唯一性

In this paper, applying the Nevanlinna theory of meromorphic function in one angular domain, we deal with a problem of uniqueness for meromorphic functions and their derivatives sharing three finite value ignoring multiplicities in an angular domain instead of the whole complex plane. Obtained results improve a recent result of Lin Weichuan and Seiki Mori.     

角域内亚纯函数的唯一性定理

该文研究了复平面上的亚纯函数在角域内分担两个集合的唯一性,将仪洪勋和林伟川最近得到的复平面上的亚纯函数在全平面上分担两个集合的唯一性定理中的在全平面上分担两个集合的条件改成在角域内分担两个集合,得到了几个唯一性定理.     

线性差分多项式的值分布

利用亚纯函数Nevanlinna理论的差分对应物,研究了亚纯函数的线性差分多项式的值分布,建立了具有最大亏量和的亚纯函数与其差分多项式的特征函数的关系,所得结果推广了现有的一些相关结果.     

On the growth of meromorphic solutions of the Schwarzian differential equations

We study the properties of meromorphic solutions of the Schwarzian differential equations in the complex plane by using some techniques from the study of the class Wp. We find some upper bounds of the order of meromorphic solutions for some types of the Schwarzian differential equations. We also show that there are no wandering domains nor Baker domains for meromorphic solutions of certain Schwarzian differential equations.     

ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH SHARED-SETS IN AN ANGULAR DOMAIN

In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.