On minimal hypersurfaces of nonnegatively Ricci curved manifolds

Yoe Itokawa

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-6

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.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:195734

DOI: 10.1155/S0161171293000705

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