A characterization of the singular time of the mean curvature flow

Cooper, Andrew

doi:10.1090/S0002-9939-2010-10714-1

A characterization of the singular time of the mean curvature flow
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Proc. Amer. Math. Soc. 139 (2011), 2933-2942 Request permission

Abstract:

In this note we investigate the behaviour at finite-time singularities of the mean curvature flow of compact Riemannian submanifolds $M_t^m\hookrightarrow (N^{m+n},h)$. We show that they are characterized by the blow-up of a trace $A=H\cdot \operatorname {II}$ of the square of the second fundamental form.

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