On minimal hypersurfaces of nonnegatively Ricci curved manifolds
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 comp...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000705 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |