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

HTML articles powered by AMS MathViewer

- by Si Duc Quang PDF
- Proc. Amer. Math. Soc.
**147**(2019), 1657-1669 Request permission

## 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 KΓ€hler manifolds into $P^{N_1}(\textbf {C})\times \cdots \times P^{N_k}(\textbf {C})$*, Japan. J. Math. (N.S.)**11**(1985), no.Β 2, 233β264. 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.Β 1, 1β18. 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.Β 10, 4329β4340. 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.Β 4, 383β398. 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.Β 9, 2701β2707. 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.Β 2, 99β138. 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.Β 2, 557β571. 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.Β 3, 355β360. MR**1117209**, DOI 10.2748/tmj/1178227459 - Manabu Shirosaki,
*On defect relations of moving hyperplanes*, Nagoya Math. J.**120**(1990), 103β112. 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.Β 44β89. 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.Β 8, 903β939. 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.Β 1, 163β179. 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.Β 2, 225β294. MR**2096455**, DOI 10.1007/BF02392741

## Additional Information

**Si Duc Quang**- Affiliation: Department of Mathematics, Hanoi National University of Education, 136-Xuan Thuy, Cau Giay, Hanoi, Vietnam β and β Thang Long Institute of Mathematics and Applied Sciences, Nghiem Xuan Yem, Hoang Mai, Hanoi, Vietnam
- Email: quangsd@hnue.edu.vn
- Received by editor(s): July 11, 2018
- Received by editor(s) in revised form: August 20, 2018
- Published electronically: January 9, 2019
- Additional Notes: This research was funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2018.01.
- Communicated by: Filippo Bracci
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 1657-1669 - MSC (2010): Primary 32H30, 32A22; Secondary 30D35
- DOI: https://doi.org/10.1090/proc/14377
- MathSciNet review: 3910430