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 On the deficiencies of meromorphic mappings of Cn into PNC

1977 ◽  
Vol 67 ◽  
pp. 165-176 ◽  
Author(s):  
Seiki Mori
Keyword(s):  
Euclidean Space ◽  
Projective Space ◽  
Complex Projective Space ◽  
Meromorphic Mapping ◽  
Meromorphic Mappings ◽  
Complex Euclidean Space ◽  
Complex Projective

Let f(z) be a non-degenerate meromorphic mapping of the n-dimensional complex Euclidean space Cn into the N-dimensional complex projective space PNC. A generalization of results of Edrei-Fuchs [2] for meromorphic mappings of C into PNC was given by Toda [5], and an estimate of K(λ) for meromorphic mappings of Cn into PNC was done by Noguchi [4]. In this note we generalize several results of Edrei-Fuchs [2] in the case of meromorphic mappings of Cn into PNC.

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 Normal families of meromorphic mappings of several complex variables for moving hypersurfaces in a complex projective space

2015 ◽  
Vol 217 ◽  
pp. 23-59
Author(s):  
Gerd Dethloff ◽  
Do Duc Thai ◽  
Pham Nguyen Thu Trang
Keyword(s):  
Projective Space ◽  
Recent Work ◽  
Complex Projective Space ◽  
Sufficient Conditions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Normal Families ◽  
Meromorphic Mappings ◽  
Meromorphic Maps ◽  
Complex Projective

AbstractThe main aim of this article is to give sufficient conditions for a family of meromorphic mappings of a domainDin ℂninto ℙN(ℂ) to be meromorphically normal if they satisfy only some very weak conditions with respect to moving hypersurfaces in ℙN(ℂ), namely, that their intersections with these moving hypersurfaces, which moreover may depend on the meromorphic maps, are in some sense uniform. Our results generalize and complete previous results in this area, especially the works of Fujimoto, Tu, Tu-Li, Mai-Thai-Trang, and the recent work of Quang-Tan.

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 Normal families of meromorphic mappings of several complex variables for moving hypersurfaces in a complex projective space

2015 ◽  
Vol 217 ◽  
pp. 23-59 ◽  
Author(s):  
Gerd Dethloff ◽  
Do Duc Thai ◽  
Pham Nguyen Thu Trang
Keyword(s):  
Projective Space ◽  
Recent Work ◽  
Complex Projective Space ◽  
Sufficient Conditions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Normal Families ◽  
Meromorphic Mappings ◽  
Meromorphic Maps ◽  
Complex Projective

AbstractThe main aim of this article is to give sufficient conditions for a family of meromorphic mappings of a domain D in ℂn into ℙN(ℂ) to be meromorphically normal if they satisfy only some very weak conditions with respect to moving hypersurfaces in ℙN(ℂ), namely, that their intersections with these moving hypersurfaces, which moreover may depend on the meromorphic maps, are in some sense uniform. Our results generalize and complete previous results in this area, especially the works of Fujimoto, Tu, Tu-Li, Mai-Thai-Trang, and the recent work of Quang-Tan.

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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