For closed smooth mean curvature flows in R^{n+1}, 3≤n≤6, at the first singular time either the mean curvature or the Morse index must blow up.
Allard, On the first variation of a varifold, Ann
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Singularities of mean curvature flow with bounded mean curvature and Morse index
For closed smooth mean curvature flows in R^{n+1}, 3≤n≤6, at the first singular time either the mean curvature or the Morse index must blow up.