Normal families of meromorphic mappings of several complex variables into $\P^{N}(\C)$

Abstract

The first aim in this article is to give some sufficient conditions for a family of meromorphic mappings of a domain $D$ in $\mathbf{C}^{n}$ into $\mathbf{P}^{N}(\mathbf{C})$ omitting hypersurfaces to be meromorphically normal. Our result is a generalization of the results of Fujimoto and Tu. The second aim is to investigate extending holomorphic mappings into the compact complex space from the viewpoint of the theory of meromorphically normal families of meromorphic mappings.