Extend Mean Curvature Flow with Finite Integral Curvature

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.

Keywords

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

2010 Mathematics Subject Classification

53C21, 53C44

Full Text (PDF format)

Published 17 April 2012