Degeneracy theorems for holomorphic mappings from a complex disc with finite growth index
Nội dung chính của bài viết
Tóm tắt
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).
Chi tiết bài viết
Từ khóa
Nevanlinna theory, holomorphic mapping, hyperplane, degeneracy theorem
Tài liệu tham khảo
[1] H. Fujimoto, Uniqueness problem with truncated multiplicities in value distribution theory, Nagoya Math. J., 152 (1998), 131-152.
[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.
[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.