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 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 Uniqueness theorem for holomorphic mappings on annuli sharing few hyperplanes

2021 ◽  
Vol 73 (2) ◽  
pp. 249-260
Author(s):  
Ha Huong Giang
Keyword(s):  
Projective Space ◽  
Uniqueness Theorem ◽  
General Condition ◽  
Complex Projective Space ◽  
Holomorphic Mappings ◽  
Complex Projective

UDC 517.5 We prove a uniqueness theorem of linearly nondegenerate holomorphic mappings from annulus to complex projective space with different multiple values and a general condition on the intersections of the inverse images of these hyperplanes.

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 Remarks to the uniqueness problem of meromorphic maps into PN(C), III

1979 ◽  
Vol 75 ◽  
pp. 71-85 ◽  
Author(s):  
Hirotaka Fujimoto
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Uniqueness Problem ◽  
Meromorphic Maps ◽  
Complex Projective

In the previous papers [3], [4], [5] the author gave some results on the uniqueness of meromorphic maps of Cn into the N-dimensional complex projective space PN(C) which have the pre-assigned inverse images for some hyperplanes in PN(C). Relating to these results, we attempt in this paper to generalize the following Cartan-Nevanlinna’s theorem to the case of meromorphic maps into PN(C).

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.

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