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.

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 Cn into PN （C）, sharing 2N ＋ 2 hyperplanes in general position, counted with multiplicities truncated by 2.

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.

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.

Some Results on the Uniqueness of Meromorphic Mappings

The authors study the problem of uniqueness of meromorphic mappings and obtain two results which partially improve two theorems of Yah and Chen in 2006.

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 PN(C),which can be seen as the improvements of previous well-known results.

Uniqueness Theorems for Meromorphic Mappings in Several Complex Variables into P^N(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.

Some Uniqueness Theorems with Truncated Multiplicities of Meromorphic Mappings

In this article, some uniqueness theorems of meromorphic mappings in sev- eral complex variables sharing hyperplanes in general position are proved with truncated multiplicities.

The Properties of Meromorphic Functions of Several Complex Variables

In this paper, by using the normality criteria for K quasimeromorphic mapping of several complex variables, we get a normality criteria for families of holomorphic functions and of meromorphic functions family.

A Uniqueness Theorem of Meromorphic Maps and a Generalization of the Borel’s Lemma

This paper gives a generalization of the classical Borel’s Lemma. Then as an application of this generalized Borel’s Lemma, a uniqueness theorem for two linearly non-degenerate meromorphic maps of Cm into P^n(C)(n ≥ 2) sharing 2n + 2 hyperplanes in general position is proved.

THE SUM OF DEFICIENCIES OF ENTIRE FUNCTION ON C^n

This paper proves that: Let / be an entire function of finite order λon Cn. Then(1) , where k(X) is a nonnegative constant depending only on A;(2) If (a, f) = 1, then A is a positive integer and equals the lower order of /.

Rational maps as Schwarzian primitives

We examine when a meromorphic quadratic differential φ with prescribed poles is the Schwarzian derivative of a rational map. We give a necessary and sufficient condition: In the Laurent series of φ around each pole c, the most singular term should take the form(1- d2)/(2(z- c)2), where d is an integer, and then a certain determinant in the next d coefficients should vanish. This condition can be optimized by neglecting some information on one of the poles(i.e., by only requiring it to be a double pole). The case d = 2 was treated by Eremenko(2012). We show that a geometric interpretation of our condition is that the complex projective structure induced by φ outside the poles has a trivial holonomy group. This statement was suggested to us by Thurston in a private communication. Our work is related to the problem of finding a rational map f with a prescribed set of critical points, since the critical points of f are precisely the poles of its Schwarzian derivative.Finally, we study the pole-dependency of these Schwarzian derivatives. We show that, in the cubic case with simple critical points, an analytic dependency fails precisely when the poles are displaced at the vertices of a regular ideal tetrahedron of the hyperbolic 3-ball.