1. bookVolumen 30 (2022): Heft 1 (February 2022)
Zeitschriftendaten
License
Format
Zeitschrift
eISSN
1844-0835
Erstveröffentlichung
17 May 2013
Erscheinungsweise
1 Hefte pro Jahr
Sprachen
Englisch
access type Uneingeschränkter Zugang

Algebraic dependence and finiteness problems of differentiably nondegenerate meromorphic mappings on Kähler manifolds

Online veröffentlicht: 12 Mar 2022
Volumen & Heft: Volumen 30 (2022) - Heft 1 (February 2022)
Seitenbereich: 271 - 294
Eingereicht: 02 Jun 2021
Akzeptiert: 31 Aug 2021
Zeitschriftendaten
License
Format
Zeitschrift
eISSN
1844-0835
Erstveröffentlichung
17 May 2013
Erscheinungsweise
1 Hefte pro Jahr
Sprachen
Englisch
Abstract

Let M be a complete Kähler manifold, whose universal covering is biholomorphic to a ball 𝔹m(R0) in ℂm (0 < R0 +∞). Our first aim in this paper is to study the algebraic dependence problem of differentiably meromorphic mappings. We will show that if k differentibility nonde-generate meromorphic mappings f1, …, fk of M into ℙn(ℂ) (n ≥ 2) satisfying the condition (Cρ) and sharing few hyperplanes in subgeneral position regardless of multiplicity then f1 Λ … Λ fk0. For the second aim, we will show that there are at most two different differentiably nondegenerate meromorphic mappings of M into ℙn(ℂ) sharing q (q ∼ 2N − n + 3 + O(ρ)) hyperplanes in N−subgeneral position regardless of multiplicity. Our results generalize previous finiteness and uniqueness theorems for differentiably meromorphic mappings of ℂm into ℙn(ℂ) and extend some previous results for the case of mappings on Kähler manifold.

MSC 2010

[1] S. J. Drouilhet, A unicity theorem for meromorphic mappings between algebraic varieties, Trans. Amer. J. Math. 265, (1981), 349–358.10.1090/S0002-9947-1981-0610953-7 Search in Google Scholar

[2] H. Fujimoto, Non-integrated defect relation for meromorphic mappings from complete Kähler manifolds intoN1 (ℂ) × … ×Nk(ℂ), Japan. J. Math. 11 (1985) 233–264.10.4099/math1924.11.233 Search in Google Scholar

[3] H. Fujimoto, A unicity theorem for meromorphic maps of a complete Khler manifold intoN (ℂ), Tohoko Math. J. 38 (1986), 327–341. Search in Google Scholar

[4] H. Fujimoto, Uniqueness problem with truncated multiplicities in value distribution theory, Nagoya Math. J. Vol. 152 (1998), 131–152.10.1017/S0027763000006826 Search in Google Scholar

[5] L. Karp, Subharmonic functions on real and complex manifolds, Math. Z. 179 (1982) 535–554.10.1007/BF01215065 Search in Google Scholar

[6] H. Fujimoto, On the Gauss mapping from a complete minimal surface inm, J. Math. Soc. Japan 35 (1983) 279–288. Search in Google Scholar

[7] J. Noguchi, A note on entire pseudo-holomorphic curves and the proof of Cartan-Nochka’s theorem, Kodai Math. J. 28 (2005) 336–34610.2996/kmj/1123767014 Search in Google Scholar

[8] S. D. Quang, Finiteness problem for meromorphic mappings sharing n+3 hyperplanes ofn(ℂ), Ann. Polon. Math. 112 (2014), no. 2, 195–215. Search in Google Scholar

[9] S. D. Quang, Algebraic relation of two meromorphic mappings on a Khler manifold having the same inverse images of hyperplanes, J. Math. Anal. Appl. 486 (2020), no. 1, 123888, 17 pp.10.1016/j.jmaa.2020.123888 Search in Google Scholar

[10] S. D. Quang, Meromorphic mappings of a complete connected Kähler manifold into a projective space sharing hyperplanes, to appear in Complex Var. Elipptic Equat. (2020), DOI: 10.1080/17476933.2020.1767088.10.1080/17476933.2020.1767088 Search in Google Scholar

[11] M. Ru and M. Sogome, Non-integrated defect relation for meromorphic mappings from complete Kähler manifolds inton(ℂ) intersecting hyper-surfaces, Trans. Amer. Math. Soc. 364 (2012), 1145–1162.10.1090/S0002-9947-2011-05512-1 Search in Google Scholar

[12] S. T. Yau, Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana U. Math. J. 25 (1976), 659–670.10.1512/iumj.1976.25.25051 Search in Google Scholar

Empfohlene Artikel von Trend MD

Planen Sie Ihre Fernkonferenz mit Scienceendo