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 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.

Approximation by Rational Mappings, via Homotopy Theory

2006 ◽  
Vol 49 (2) ◽  
pp. 237-246 ◽  
Author(s):  
P. M. Gauthier ◽  
E. S. Zeron
Keyword(s):  
Euclidean Space ◽  
Projective Space ◽  
Complex Projective Space ◽  
Homotopy Theory ◽  
Continuous Mappings ◽  
Complex Euclidean Space ◽  
Complex Projective ◽  
Compact Subsets

AbstractContinuous mappings defined from compact subsets K of complex Euclidean space ℂn into complex projective space ℙm are approximated by rational mappings. The fundamental tool employed is homotopy theory.

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 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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