Gerd Dethloff

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.

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.

Normal families of meromorphic mappings of several complex variables for moving hypersurfaces in a complex projective space

The main aim of this article is to give some sufficient conditions for a family of meromorphic mappings on a domain D in C^n into P^N(C) to be meromorphically normal if they satisfy only some very weak conditions with respect to moving hypersurfaces in P^N(C), namely that their intersections with these moving hypersurfaces, which may moreover depend on the meromorphic maps, are in some sense uniform. Our results generalise and complete previous results in this area, especially the works of Fujimoto, Tu, Tu-Li, Mai-Thai-Trang and the recent work of Quang-Tan.