Higher-Dimensional Generalizations of Some Theorems on Normality of Meromorphic Functions

In [5], Grahl and Nevo obtained a significant improvement for the well-known normality criterion of Montel. They proved that for a family of meromorphic functions F in a domain D subset of C, and for a positive constant epsilon if for each f. F there exist meromorphic functions a(f), b(f), c(f) such that f omits a(f), b(f), c(f) in D and [GRAPHICS] for all z is an element of D, then F is normal in D. Here, rho is the spherical metric in C. In this paper, we establish the high-dimensional versions for the above result and for the following well-known result of Lappan: A meromorphic function f in the unit disc triangle := {z. C : |z| < 1} is normal if there are five distinct values a(1),..., a(5) such that [GRAPHICS]