International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 573-578
On minimal hypersurfaces of nonnegatively Ricci curved manifolds
Department of Mathematics, University of Alabama at Birmingham, Birmingham 35294, Alabama, USA
Received 3 March 1992; Revised 1 June 1992
Copyright © 1993 Yoe Itokawa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider a complete open riemannian manifold of nonnegative Ricci curvature and a rectifiable hypersurface in which
satisfies some local minimizing property. We prove a structure
theorem for and a regularity theorem for . More precisely, a
covering space of 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.