Normal families of meromorphic mappings of several complex variables into CPⁿfor moving hypersurfaces

Abstract

Abstract. We prove some normality criteria for families of meromorphic mappings of a domain D ⊂ C m into CP n under a condition on the inverse images of moving hypersurfaces.

Weak normal and quasinormal families of holomorphic curves

“…, f nN ) on ∆(p, r). Then for every > 0, there exists a positive integer n 0 such that for all n > n 0 we have (12) max…”

“…By the definition of M , we have f n (z) < M and g(z) < M for all z ∈ ∆(p, r 1 ). Therefore, (12) implies that…”

“…With respect to the notion of meromorphic convergence, there are many results on the meromorphic normality of meromorphic mappings established in some recent years, e.g., [4,6,12].…”

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

“…There are only a few such results in some restricted situations (see [11], [22]). For instance, we recall a recent result of Quang and Tan [11] which is the best result available at present and which generalizes [22,Theorem 2.2].…”

“…Theorem B ( [11,Theorem 1.4]). Let F be a family of meromorphic mappings of a domain D ⊂ C n into P N (C), and let Q 1 , .…”