Normal family of meromorphic mappings and Big Picard's theorem

TL;DR

This paper advances the theory of normal families of meromorphic mappings in several complex variables, extending classical results like Montel's criterion and providing new insights into the extension and behavior of such mappings.

Contribution

It significantly extends Montel's normal criterion for meromorphic mappings in multiple variables and improves understanding of their extension properties.

Findings

Extended Montel's criterion to several variables.

Established new results on the extension of holomorphic mappings.

Provided conditions for normality involving moving hypersurfaces.

Abstract

In this paper, we prove some results in normal family of meromorphic mappings intersecting with moving hypersurfaces. As some applications, we establish some results for normal mapping and extension of holomorphic mappings. A our result is strongly extended the Montel's normal criterion in the case several variables which is due to Tu in [Proc. Amer. Math. Soc. 127,1039-1049, 1999]. Our results are also strongly extended the results of Tu-Li in [Sci. China Ser. A. 48, 355-364, 2005] and [J. Math. Anal. Appl. 342, 629-638, 2006].