We consider a complete open riemannian manifold M of nonnegative Ricci curvature and a rectifiable hypersurface ∑ in M which
satisfies some local minimizing property. We prove a structure
theorem for M and a regularity theorem for ∑. More precisely, a
covering space of M is shown to split off a compact domain and ∑ is
shown to be a smooth totally geodesic submanifold. This generalizes
a theorem due to Kasue and Meyer.