The mean curvature flow (MCF) is a quasilinear parabolic equation; hence solutions are expected to develop singularities in finite time. It is straightforward that the second fundamental form must blow up at such a finite-time singularity.

This talk will address whether it is possible to characterise the singular time by a weaker criterion. I will show that in MCF the second fundamental form must blow up, roughly speaking, in the direction of the mean curvature vector. Time permitting, I will give two independent proofs that under a mildness assumption for the singularity, the mean curvature vector itself must blow up, and mention connections to some results for the Ricci flow.