Tran Van Tan

Uniqueness problem for meromorphic mappings with truncated multiplicities and moving targets

In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of C^m into P^n with (3n+1) moving targets and truncated multiplicities.

MEROMORPHIC FUNCTIONS SHARING SMALL FUNCTIONS AS TARGETS

The purpose of this article is twofold. The first is to prove the unicity theorem with truncated multiplicities of meromorphic functions sharing five small functions. This gives a remarkable improvement of the results of Yuhua–Jianyong, Yao and Yi. The second is to generalize the unicity theorem of Fujimoto to meromorphic functions sharing four small functions with truncated multiplicities.

A uniqueness theorem for meromorphic maps with moving hypersurfaces

In this paper, we establish a uniqueness theorem for algebraically nondegenerate meromorphic maps of C^m into C P^n and slowly moving hypersurfaces Q_j in C P^n, j=1,...,q in (weakly) general position, where q depends effectively on n and on the degrees d_j of the hypersurfaces Q_j.

A unisqueness theorem for meromorphic mappings with two families of hyperplanes

The uniqueness problem of meromorphic mappings under a condition on the inverse images of divisors was first studied by Nevanlinna [6]. He showed that for two nonconstant meromorphic functions f and g on the complex plane C, if they have the same inverse images for five distinct values, then f ≡ g. In 1975, Fujimoto [3] generalized Nevanlinna’s result to the case of meromorphic mappings of C into CP . He showed that for two linearly nondegenerate meromorphic mappings f and g of C into CP , if they have the same inverse images counted with multiplicities for (3n+ 2) hyperplanes in general position in CP , then f ≡ g. In 1983, Smiley [9] showed that

AN EXTENSION OF THE CARTAN-NOCHKA SECOND MAIN THEOREM FOR HYPERSURFACES

In 1983, Nochka proved a conjecture of Cartan on defects of holomorphic curves in ℂPn relative to a possibly degenerate set of hyperplanes. In this paper, we generalize Nochkas theorem to the case of curves in a complex projective variety intersecting hypersurfaces in subgeneral position. Further work will be needed to determine the optimal notion of subgeneral position under which this result can hold, and to lower the effective truncation level which we achieved.

A DEGENERACY THEOREM FOR MEROMORPHIC MAPPINGS WITH MOVING TARGETS

The purpose of this article is to prove a degeneracy theorem for meromorphic mappings of ℂm into ℂPn with (2n + 2) moving targets.

A note on the uniqueness problem of non-Archimedean holomorphic curves

We prove a uniqueness theorem for non-Archimedean linearly nondegenerate holomorphic curves in projective spaces of dimension

Normal families of meromorphic mappings sharing hypersurfaces

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