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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| Format: | Article |
| Language: | English |
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Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171293000705 |
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| _version_ | 1832558710502719488 |
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| author | Yoe Itokawa |
| author_facet | Yoe Itokawa |
| author_sort | Yoe Itokawa |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2b793361d492413aa2dcf7a5d67a15b9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2b793361d492413aa2dcf7a5d67a15b92025-02-03T01:31:43ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116357357810.1155/S0161171293000705On minimal hypersurfaces of nonnegatively Ricci curved manifoldsYoe Itokawa0Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294, USAWe 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.http://dx.doi.org/10.1155/S0161171293000705riemannian manifoldnonnegative Ricci curvatureminimal hypersurfaceintegral currents. |
| spellingShingle | Yoe Itokawa On minimal hypersurfaces of nonnegatively Ricci curved manifolds International Journal of Mathematics and Mathematical Sciences riemannian manifold nonnegative Ricci curvature minimal hypersurface integral currents. |
| title | On minimal hypersurfaces of nonnegatively Ricci curved manifolds |
| title_full | On minimal hypersurfaces of nonnegatively Ricci curved manifolds |
| title_fullStr | On minimal hypersurfaces of nonnegatively Ricci curved manifolds |
| title_full_unstemmed | On minimal hypersurfaces of nonnegatively Ricci curved manifolds |
| title_short | On minimal hypersurfaces of nonnegatively Ricci curved manifolds |
| title_sort | on minimal hypersurfaces of nonnegatively ricci curved manifolds |
| topic | riemannian manifold nonnegative Ricci curvature minimal hypersurface integral currents. |
| url | http://dx.doi.org/10.1155/S0161171293000705 |
| work_keys_str_mv | AT yoeitokawa onminimalhypersurfacesofnonnegativelyriccicurvedmanifolds |