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.
"Extend Mean Curvature Flow with Finite Integral Curvature." Asian J. Math. 15 (4) 549 - 556, December 2011.