Normal Families of Meromorphic Functions in Several Variables

We extend the well-known Gu’s normality criterion for meromorphic functions of one complex variable to the case of several complex variables. Let ℱ be a family of functions meromorphic on a given domain D⊂ℂ^n , k a positive integer and a∈ (ℂ∖{0})^n a point. If for every function f∈ℱ , all of its zeros have multiplicity at least k+2 and the partial derivatives ∇ ^kf≠a on D , then the family ℱ is normal in D .