scholarly journals Uniqueness polynomials for holomorphic curves into the complex projective space

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 351-356
Author(s):  
Liu Yang
Keyword(s):  
Projective Space ◽  
Complex Plane ◽  
Complex Projective Space ◽  
Meromorphic Functions ◽  
Holomorphic Curves ◽  
Complex Projective

In this paper, by making use of uniqueness polynomials for meromorphic functions, we obtain a class of uniqueness polynomials for holomorphic curves from the complex plane into complex projective space. The related uniqueness problems are also considered.

scholarly journals The uniqueness problem of meromorphic maps into the complex projective space

1975 ◽  
Vol 58 ◽  
pp. 1-23 ◽  
Author(s):  
Hirotaka Fujimoto
Keyword(s):  
Projective Space ◽  
Complex Plane ◽  
Complex Projective Space ◽  
Meromorphic Functions ◽  
Uniqueness Problem ◽  
Meromorphic Maps ◽  
Complex Projective

In 1921, G. Pólya showed that non-constant meromorphic functions ϕ and ψ of finite genera on the complex plane C are necessarily equal if there are distinct five values ai(1 ≦ i ≦ 5) such that ϕ(z) — ai and ψ(z) — ai have the same zeros of the same multiplicities for each i ([8]). Afterwards, R. Nevanlinna obtained the same conclusion for arbitrary ϕp and ψ satisfying ϕ— 1(ai) = ψ— 1(1 ≦ i ≦ 5) regardless of multiplicities. And, some other results relating to this were given by H. Cartan ([2], [3]), E. M. Schmid ([9]) and others. The purpose of this paper is to give some types of generalizations of these results to the case of meromorphic maps into the N-dimensional complex projective space PN(C).

scholarly journals A uniqueness theorem of algebraically non-degenerate meromorphic maps into PN(C)

1976 ◽  
Vol 64 ◽  
pp. 117-147 ◽  
Author(s):  
Hirotaka Fujimoto
Keyword(s):  
Projective Space ◽  
Uniqueness Theorem ◽  
Complex Projective Space ◽  
Meromorphic Functions ◽  
Uniqueness Theorems ◽  
Meromorphic Maps ◽  
Complex Projective

In the previous paper [3], the author generalized the uniqueness theorems of meromorphic functions given by G. Pólya in [5] and R. Nevanlinna in [4] to the case of meromorphic maps of Cn into the N- dimensional complex projective space PN(C).

scholarly journals On families of meromorphic maps into the complex projective space

1974 ◽  
Vol 54 ◽  
pp. 21-51 ◽  
Author(s):  
Hirotaka Fujimoto
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Meromorphic Functions ◽  
Normal Family ◽  
Analytic Subset ◽  
Several Variables ◽  
Meromorphic Maps ◽  
Complex Projective ◽  
Quasinormal Family

In [10], P. Montel defined the notion of a quasinormal family of meromorphic functions and obtained several results relating to this. Afterwards, in [13], H. Rutishauser generalized some of them to the case of meromorphic functions of several variables. By definition, a quasi-normal family of meromorphic functions on a domain D in Cn is a family such that any sequence in has a subsequence which converges compactly outside a thin analytic subset of D.

scholarly journals A relation between order and defects of meromorphic mappings of Cn into Pn(C)

1975 ◽  
Vol 59 ◽  
pp. 97-106 ◽  
Author(s):  
Junjiro Noguchi
Keyword(s):  
Characteristic Function ◽  
Projective Space ◽  
Complex Plane ◽  
Complex Projective Space ◽  
Counting Function ◽  
Meromorphic Mapping ◽  
Meromorphic Mappings ◽  
Complex Projective

Let f be a meromorphic mapping of the n-dimensional complex plane Cn into the N-dimensional complex projective space PN(C). We denote by T(r,f) the characteristic function of f and by N(r,f*H) the counting function for a hyperplane H ⊂ PN(C). The purpose of this paper is to establish the following results.

scholarly journals Hyperbolicity of the complement of arrangements of non complex lines

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 3109-3118
Author(s):  
Fathi Haggui ◽  
Abdessami Jalled
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
The Other ◽  
Holomorphic Curves ◽  
Real Dimension ◽  
Kobayashi Hyperbolicity ◽  
Other Hand ◽  
Complex Lines ◽  
Complex Projective ◽  
Real Subspace

The goal of this paper is twofold. We study holomorphic curves f:C ? C3 avoiding four complex hyperplanes and a real subspace of real dimension five in C3 where we study the cases where the projection of f into the complex projective space CP2 is constant. On the other hand, we investigate the kobayashi hyperbolicity of the complement of five perturbed lines in CP2.

scholarly journals From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space

2002 ◽  
Vol 66 (3) ◽  
pp. 465-475 ◽  
Author(s):  
J. Bolton ◽  
C. Scharlach ◽  
L. Vrancken
Keyword(s):  
Projective Space ◽  
Minimal Surface ◽  
Complex Projective Space ◽  
Lagrangian Submanifold ◽  
3 Dimensional ◽  
Ellipse Of Curvature ◽  
Complex Projective

In a previous paper it was shown how to associate with a Lagrangian submanifold satisfying Chen's equality in 3-dimensional complex projective space, a minimal surface in the 5-sphere with ellipse of curvature a circle. In this paper we focus on the reverse construction.

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