arXiv subjects

Le Ngoc Quynh

Publications and source records attributed to Le Ngoc Quynh.

5 recordsLinked to original sources

arXiv2020

Non-integrated defect relation for meromorphic mappings from a Kähler manifold with hypersurfaces of a projective variety in subgeneral position

In this paper, we establish a truncated non-integrated defect relation for meromorphic mappings from a complete Kähler manifold into a projective variety intersecting a family of hypersurfaces located in subgeneral position, where the truncation level of the defect is explicitly estimated. Our result generalizes and improves previous ones. In particular, when the family of hypersurfaces located in general position, our theorem will implies the previous result of Min Ru-Sogome. In the last part of this paper we will apply ours to study the distribution of the Gauss map of minimal surfaces.

math.CV↗

arXiv2016

Uniqueness problem of meromorphic mappings from a complete Kähler manifold into a projective variety

The purpose of this paper has twofold. The first is to prove a unicity theorem for meromorphic mappings of a complete Kähler manifold M in P^n(C) sharing few hypersurfaces. The second is to give a unicity theorem for the case of differential nondegenerate meromorphic mappings sharing 2N-n+3+2ρ(2N-n+1) hyperplanes in N subgeneral position.

math.CV↗

arXiv2016

Two meromorphic mappings having the same inverse images of moving hyperplanes

In this paper, we will show that if two meromorphic mappings $f$ and $g$ of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ have the same inverse images for $(2n+2)$ moving hyperplanes $\{a_i\}_{i=1}^{2n+2}$ with multiplicities counted to level $l_0$ then the map $f\times g$ must be algebraically degenerated over the field $\mathcal R\{a_i\}_{i=1}^{2n+2}$, where $l_0=3n^3(n+1)q(q-2)$ with $q=\binom{2n+2}{n+2}$. Our result generalizes the previous result for fixed hyperplanes case of Fujimoto and also improves his result by giving an explicit estimate for the number $l_0$.

math.CV↗

arXiv2016

Algebraic dependences and uniqueness problem of meromorphic mappings sharing moving hyperplanes without counting multiplicities

This article deals with the multiple values and algebraic dependences problem of meromorphic mappings sharing moving hyperplanes in projective space. We give some algebraic dependences theorems for meromorphic mappings sharing moving hyperplanes without counting multiplicity, where all zeros with multiplicities more than a certain number are omitted. Basing on these results, some unicity theorems regardless of multiplicity for meromorphic mappings in several complex variables are given. These results are extensions and strong improvements of some recent results.

math.CV↗

arXiv2013

Two meromorphic mappings sharing 2n + 2 hyperplanes regardless of multiplicity

Nevanlinna showed that two non-constant meromorphic functions on $\mathbb C$ must be linked by a Möbius transformation if they have the same inverse images counted with multiplicities for four distinct values. After that this results is generalized by Gundersen to the case where two meromorphic functions share two values ignoring multiplicity and share other two values with multiplicities trucated by 2. Previously, the first author proved that for $n\ge 2,$ there are at most two linearly nondegenerate meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ sharing $2n+2$ hyperplanes ingeneral position ignoring multiplicity. In this article, we will show that if two meromorphic mappings $f$ and $g$ of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ share $2n+1$ hyperplanes ignoring multiplicity and another hyperplane with multiplicities trucated by $n+1$ then the map $f\times g$ is algebraically degenerate.

math.CV↗