Some extensions of the mean curvature flow in Riemannian manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2010
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| _version_ | 1866918396019343360 |
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| author | Wu, Jia-Yong |
| author_facet | Wu, Jia-Yong |
| contents | Given a family of smooth immersions $F_t: M^n\to N^{n+1}$ of closed hypersurfaces in a locally symmetric Riemannian manifold $N^{n+1}$ with bounded geometry, moving by the mean curvature flow, we show that at the first finite singular time of the mean curvature flow, certain subcritical quantities concerning the second fundamental form blow up. This result not only generalizes a recent result of Le-Sesum and Xu-Ye-Zhao, but also extends the latest work of N. Le in the Euclidean case (arXiv: math.DG/1002.4669v2). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1006_5177 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | Some extensions of the mean curvature flow in Riemannian manifolds Wu, Jia-Yong Differential Geometry Analysis of PDEs 53C40, 57R42 Given a family of smooth immersions $F_t: M^n\to N^{n+1}$ of closed hypersurfaces in a locally symmetric Riemannian manifold $N^{n+1}$ with bounded geometry, moving by the mean curvature flow, we show that at the first finite singular time of the mean curvature flow, certain subcritical quantities concerning the second fundamental form blow up. This result not only generalizes a recent result of Le-Sesum and Xu-Ye-Zhao, but also extends the latest work of N. Le in the Euclidean case (arXiv: math.DG/1002.4669v2). |
| title | Some extensions of the mean curvature flow in Riemannian manifolds |
| topic | Differential Geometry Analysis of PDEs 53C40, 57R42 |
| url | https://arxiv.org/abs/1006.5177 |