On minimal hypersurfaces of nonnegatively Ricci curved manifolds

Abstract

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.

Keywords

• riemannian manifold
• nonnegative Ricci curvature
• minimal hypersurface
• integral currents.