Asian Journal of Mathematics

Volume 15 (2011)

Number 4

Extend Mean Curvature Flow with Finite Integral Curvature

Pages: 549 – 556



Hong-Wei Xu

Fei Ye

En-Tao Zhao


In this note, we prove that the solution of certain mean curvature flow on a finite time interval [0, T) can be extended over time T if the space-time integration of the mean curvature is finite. Moreover, we show that the condition is optimal in some sense.


Mean curvature flow; maximal existence time; second fundamental form; integral curvature

2010 Mathematics Subject Classification

53C21, 53C44

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