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Date Published:
23/06/2024
Online Published:
23/06/2024
Online Published:
21/05/2024
Abstract Views: 20
Views PDF: 31
Views PDF: 31
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Articles
How to Cite
Nguyen Thi, N. (2024). Degeneracy theorems for holomorphic mappings from a complex disc with finite growth index. Thang Long Journal of Science: Mathematics and Mathematical Sciences, 3(1). https://science.thanglong.edu.vn/index.php/volc/article/view/122
Degeneracy theorems for holomorphic mappings from a complex disc with finite growth index
Main Article Content
Abstract
Abstract. In this paper, we prove degeneracy theorems for holomorphic
mappings from a complex disc Δ(R) ⊂ C with finite growth index into
Pn(C) sharing hyperplanes in general position. We further consider the
case that intersecting points of the mappings and the hyperplanes with
multiplicities more than a certain number do not need to be counted.
These results generalize the previous degeneracy theorems for meromorphic
mappings from Cm into Pn(C).
Article Details
Keywords
Nevanlinna theory, holomorphic mapping, hyperplane, degeneracy theorem
References
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[3] N. T. Nhung and L. N. Quynh, Degeneracy theorems for three meromorphic mappings sharing few hyperplanes, Houston J. Math., 44 (2018),
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369–391.
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in Publ. Math. Debrecen.
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[9] M. Ru and N. Sibony, The second main theorem in the hyperbolic case, Math. Annalen, 377 (2020), 759–795.
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560.
[2] S. Ji, Uniqueness problem without multiplicities in value distribution theory, Pacific J. Math. 135 (1988), 323-348.
[3] N. T. Nhung and L. N. Quynh, Degeneracy theorems for three meromorphic mappings sharing few hyperplanes, Houston J. Math., 44 (2018),
437–454.
[4] S. D. Quang, Unicity of meromorphic mappings sharing few hyperplanes, Ann. Pol. Math., 102 No. 3 (2011), 255-270.
[5] S. D. Quang, A Finiteness theorem for meromorphic mappings with few hyperplanes, Kodai Math. J., 35 (2012), 463-484.
[6] S. D. Quang, Degeneracy and finiteness problems for holomorphic curves from a disc into Pn(C) with finite growth index, Kodai Math. J., 44 (2021),
369–391.
[7] S. D. Quang, Degeneracy theorems for meromorphic mappings of complete K¨ahler manifolds sharing hyperplanes in projective spaces, To appear
in Publ. Math. Debrecen.
[8] S. D. Quang and L. N. Quynh, Algebraic dependences of meromorphic mappings sharing few hyperplanes without counting multiplicity, Kodai
Math. J., 38 (2015) 97-118.
[9] M. Ru and N. Sibony, The second main theorem in the hyperbolic case, Math. Annalen, 377 (2020), 759–795.
[10] Q. Yan and Z. Chen, A degeneracy theorem for meromorphic mappings with truncated multiplicities, Acta Mathematica Scientia, 31 2011, 549-
560.