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 ℝ N . 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 codimension n meeting any n-plane passing through the origin in at most k points has no more c(n, N)k ends. © 1994 Springer-Verlag.