Finiteness of the number of ends of minimal submanifolds in Euclidean space

We prove a version of the well-known Denjoy-Ahlfors theorem about the number of asymptotic values of an entire function for properly immersed minimal surfaces of arbitrary codimension in ℝN. The finiteness of the number of ends is proved for minimal submanifolds with finite projective volume. We show, as a corollary, that a minimal surface of codimensionn meeting anyn-plane passing through the origin in at mostk points has no morec(n, N)k ends