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International Journal of Mathematics and Mathematical Sciences
Volume 16, Issue 3, Pages 573-578
http://dx.doi.org/10.1155/S0161171293000705

On minimal hypersurfaces of nonnegatively Ricci curved manifolds

Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294, USA

Received 3 March 1992; Revised 1 June 1992

Copyright © 1993 Hindawi Publishing Corporation. 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.

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.