Second main theorems for meromorphic mappings and moving hyperplanes with truncated counting functions

Duc Quang, Si

doi:10.1090/proc/14377

Second main theorems for meromorphic mappings and moving hyperplanes with truncated counting functions
HTML articles powered by AMS MathViewer

by Si Duc Quang

Proc. Amer. Math. Soc. 147 (2019), 1657-1669

DOI: https://doi.org/10.1090/proc/14377

Published electronically: January 9, 2019

PDF | Request permission

Erratum: Proc. Amer. Math. Soc. 148 (2020), 3195-3197.

Abstract:

In this article, we establish some new second main theorems for meromorphic mappings of $\mathbf {C}^m$ into $\mathbf {P}^n(\mathbf {C})$ and moving hyperplanes with truncated counting functions. Our results are improvements of the previous second main theorems for moving hyperplanes with truncated (to level $n$) counting functions.

References

Hirotaka Fujimoto, Nonintegrated defect relation for meromorphic maps of complete Kähler manifolds into $P^{N_1}(\textbf {C})\times \cdots \times P^{N_k}(\textbf {C})$, Japan. J. Math. (N.S.) 11 (1985), no. 2, 233–264. MR 884636, DOI 10.4099/math1924.11.233
Junjiro Noguchi and Takushiro Ochiai, Geometric function theory in several complex variables, Translations of Mathematical Monographs, vol. 80, American Mathematical Society, Providence, RI, 1990. Translated from the Japanese by Noguchi. MR 1084378, DOI 10.1090/mmono/080
Si Duc Quang, Second main theorems for meromorphic mappings intersecting moving hyperplanes with truncated counting functions and unicity problem, Abh. Math. Semin. Univ. Hambg. 86 (2016), no. 1, 1–18. MR 3474505, DOI 10.1007/s12188-015-0114-1
Si Duc Quang, Second main theorems with weighted counting functions and algebraic dependence of meromorphic mappings, Proc. Amer. Math. Soc. 144 (2016), no. 10, 4329–4340. MR 3531183, DOI 10.1090/proc/13061
Si Duc Quang and Do Phuong An, Unicity of meromorphic mappings sharing few moving hyperplanes, Vietnam J. Math. 41 (2013), no. 4, 383–398. MR 3142403, DOI 10.1007/s10013-013-0035-1
Min Ru, A uniqueness theorem with moving targets without counting multiplicity, Proc. Amer. Math. Soc. 129 (2001), no. 9, 2701–2707. MR 1838794, DOI 10.1090/S0002-9939-01-06040-3
Min Ru and Wilhelm Stoll, The second main theorem for moving targets, J. Geom. Anal. 1 (1991), no. 2, 99–138. MR 1113373, DOI 10.1007/BF02938116
Min Ru and Julie Tzu-Yueh Wang, Truncated second main theorem with moving targets, Trans. Amer. Math. Soc. 356 (2004), no. 2, 557–571. MR 2022710, DOI 10.1090/S0002-9947-03-03453-6
Manabu Shirosaki, Another proof of the defect relation for moving targets, Tohoku Math. J. (2) 43 (1991), no. 3, 355–360. MR 1117209, DOI 10.2748/tmj/1178227459
Manabu Shirosaki, On defect relations of moving hyperplanes, Nagoya Math. J. 120 (1990), 103–112. MR 1086573, DOI 10.1017/S0027763000003287
Bernard Shiffman, Introduction to the Carlson-Griffiths equidistribution theory, Value distribution theory (Joensuu, 1981) Lecture Notes in Math., vol. 981, Springer, Berlin-New York, 1983, pp. 44–89. MR 699133
Do Duc Thai and Si Duc Quang, Uniqueness problem with truncated multiplicities of meromorphic mappings in several complex variables for moving targets, Internat. J. Math. 16 (2005), no. 8, 903–939. MR 2168074, DOI 10.1142/S0129167X05003132
Duc Thai Do and Duc Quang Si, Second main theorem with truncated counting function in several complex variables for moving targets, Forum Math. 20 (2008), no. 1, 163–179. MR 2386785, DOI 10.1515/FORUM.2008.007
Katsutoshi Yamanoi, The second main theorem for small functions and related problems, Acta Math. 192 (2004), no. 2, 225–294. MR 2096455, DOI 10.1007/BF02392741