以较低截断重数分担超平面的亚纯映射的唯一性问题
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摘要
首先证明了一些以较低截断重数分担2n+2个超平面的亚纯映射的唯一性定理.最后一章给出了在条件f~(-1)(H_j)■g~(-1)(H_j)及q≥2n+3下的一个唯一性定理的简单证明.
In this paper, we prove first some uniqueness theorems for two meromorphic maps sharing 2 n + 2 hyperplanes with low truncated multiplicities. And in the last section, we give a simple proof of a uniqueness theorem under the assumption that f~(-1)(H_j)■g~(-1)(H_j) and q≥2 n+3.
In this paper, we prove first some uniqueness theorems for two meromorphic maps sharing 2 n + 2 hyperplanes with low truncated multiplicities. And in the last section, we give a simple proof of a uniqueness theorem under the assumption that f~(-1)(H_j)■g~(-1)(H_j) and q≥2 n+3.
引文
[1] Cao H Z, Cao T B. Uniqueness problem for meromorphic mappings in several complex variables with few hyperplanes. Acta Math Sin, 2015, 31(8):1327-1338
[2] Chen Z H, Yan Q M. Uniqueness theorem of meromorphic mappings into P~N(C)sharing 2N+3 hyperplanes regardless of multiplicities. Int J Math, 2009, 20(6):717-726
[3] Chen Z H, Yan Q M. A note on uniqueness problem for meromorphic mappings with 2N+3 hyperplanes.Sci China Math, 2010, 53(10):2657-2663
[4] Dethloff G, Si D Q, Tan T V. A uniqueness theorem for meromorphic mappings with two families of hyperplanes. Proc Amer Math Soc, 2012, 140(1):189-197
[5] Fujimoto H. The uniqueness problem of meromorphic maps into the complex projective space. Nagoya Math J, 1975, 58:1-23
[6] Fujimoto H. A uniqueness theorem of algebraically non-degenerate meromorphic maps into P~N(C). Nagoya Math J, 1976, 64:117-147
[7] Fujimoto H. Uniqueness problem with truncated multiplicities in value distribution theory. Nagoya Math J, 1998, 152:131-152
[8] Quang S D. Unicity of meromorphic mappings sharing few hyperplanes. Ann Polon Math, 2011, 102(3):255-270
[9] Smiley L. Geometric conditions for unicity of holomorphic curves. Contemp Math, 1983, 25:149-154
[10] Si D Q. Some extensions of the four values theorem of Nevanlinna-Gundersen. Kodai Math J, 2013, 36:579-595
[11] Thai D D, Quang S D. Uniqueness problem with truncated multiplicities of meromorphic mappings in several complex variables. Int J Math, 2006, 17(10):1223-1257
[12] Wong P M, Stoll W. Second main theorem of Nevanlinna theory for nonequidimensional meromorphic maps. Amer J Math, 1994, 116(5):1031-1071
[2] Chen Z H, Yan Q M. Uniqueness theorem of meromorphic mappings into P~N(C)sharing 2N+3 hyperplanes regardless of multiplicities. Int J Math, 2009, 20(6):717-726
[3] Chen Z H, Yan Q M. A note on uniqueness problem for meromorphic mappings with 2N+3 hyperplanes.Sci China Math, 2010, 53(10):2657-2663
[4] Dethloff G, Si D Q, Tan T V. A uniqueness theorem for meromorphic mappings with two families of hyperplanes. Proc Amer Math Soc, 2012, 140(1):189-197
[5] Fujimoto H. The uniqueness problem of meromorphic maps into the complex projective space. Nagoya Math J, 1975, 58:1-23
[6] Fujimoto H. A uniqueness theorem of algebraically non-degenerate meromorphic maps into P~N(C). Nagoya Math J, 1976, 64:117-147
[7] Fujimoto H. Uniqueness problem with truncated multiplicities in value distribution theory. Nagoya Math J, 1998, 152:131-152
[8] Quang S D. Unicity of meromorphic mappings sharing few hyperplanes. Ann Polon Math, 2011, 102(3):255-270
[9] Smiley L. Geometric conditions for unicity of holomorphic curves. Contemp Math, 1983, 25:149-154
[10] Si D Q. Some extensions of the four values theorem of Nevanlinna-Gundersen. Kodai Math J, 2013, 36:579-595
[11] Thai D D, Quang S D. Uniqueness problem with truncated multiplicities of meromorphic mappings in several complex variables. Int J Math, 2006, 17(10):1223-1257
[12] Wong P M, Stoll W. Second main theorem of Nevanlinna theory for nonequidimensional meromorphic maps. Amer J Math, 1994, 116(5):1031-1071