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| On the Conditions of Extending Mean Curvature Flow |
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Citation： |
Xinrong JIANG,Caisheng LIAO.On the Conditions of Extending Mean Curvature Flow[J].Chinese Annals of Mathematics B,2012,33(1):61~72 |
| Page view： 2623
Net amount： 2210 |
Authors： |
Xinrong JIANG; Caisheng LIAO; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10871069, 10871070) and the Shanghai Leading Academic Discipline Project (No. B407). |
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| Abstract： |
The authors consider a family of smooth immersions F( ? , t) : Mn → Rn+1 ofclosed hypersurfaces in Rn+1 moving by the mean curvature flow ?F(p,t)?t = ?H(p, t)?ν(p, t)for t ∈ [0, T). They show that if the norm of the second fundamental form is boundedabove by some power of mean curvature and the certain subcritical quantities concerningthe mean curvature integral are bounded, then the flow can extend past time T. The resultis similar to that in [6–9]. |
Keywords： |
Mean curvature flow, Moser iteration, Type I singularity |
Classification： |
53C44,35K55 |
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