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| The Extension of the Hk Mean Curvature Flow inRiemannian Manifolds? |
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Citation： |
Hongbing QIU,Yunhua YE,Anqiang ZHU.The Extension of the Hk Mean Curvature Flow inRiemannian Manifolds?[J].Chinese Annals of Mathematics B,2014,35(2):191~208 |
| Page view： 1784
Net amount： 1611 |
Authors： |
Hongbing QIU; Yunhua YE; Anqiang ZHU; |
Foundation： |
National Natural Science Foundation of China (Nos. 11301399, 11126189,11171259, 11126190), the Specialized Research Fund for the Doctoral Program of Higher Education(No. 20120141120058), the China Postdoctoral Science Foundation (No. 20110491212) and the FundamentalResearch Funds for the Central Universities (Nos. 2042011111054, 20420101101025). |
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| Abstract： |
In this paper, the authors consider a family of smooth immersions Ft : Mn →
Nn+1 of closed hypersurfaces in Riemannian manifold Nn+1 with bounded geometry, moving
by the Hk mean curvature flow. The authors show that if the second fundamental form
stays bounded from below, then the Hk mean curvature flow solution with finite total mean
curvature on a finite time interval [0, Tmax) can be extended over Tmax. This result generalizes
the extension theorems in the paper of Li (see “On an extension of the Hk mean
curvature flow, Sci. China Math., 55, 2012, 99–118”). |
Keywords： |
Hk mean curvature flow, Riemannian manifold, Sobolev type inequality,Moser iteration |
Classification： |
53C44, 53C21 |
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