Compactness of certain families of pseudo-holomorphic mappings into C-n

Abstract

We present a normal family theorem for injective almost holomorphic maps from a manifold with almost complex structures into C-n. Our theorem implies a new consequence even for the holomorphic mappings of a complex manifold into C-n, which can be seen as a generalization of the convergence theorem for Frankel's scaling sequence whose images are not necessarily convex. Moreover, our method is closer in spirit to the circle of ideas centered around the classical Montel theorem.