Big Picard's theorems for holomorphic mappings of several complex variables into PN(C) with moving hyperplanes

Motivated by the accomplishment of the second main theorem with moving targets, many authors studied the moving target problems in value distribution theory and related topics. In this paper, we prove some big Picard's theorems for holomorphic mappings of several complex variables into PN(C) with moving hyperplanes, related to Nochka's little Picard-type theorems. As its application, we give a new quasi-normal criterion for families of meromorphic mappings of several complex variables into PN(C) with moving hyperplanes. The new results in this paper greatly improve some earlier related results.