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

Abstract

The main aim of this article is to give sufficient conditions for a family of meromorphic mappings of a domain $D$ in ${\mathbb{C}}^n$ into ${\mathbb{P}}^N\left(\mathbb{C}\right)$ to be meromorphically normal if they satisfy only some very weak conditions with respect to moving hypersurfaces in ${\mathbb{P}}^N\left(\mathbb{C}\right)$, namely, that their intersections with these moving hypersurfaces, which moreover may depend on the meromorphic maps, are in some sense uniform. Our results generalize 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.