On the Mean Convexity of a Space-and-Time Neighborhood of Generic Singularities Formed by Mean Curvature flow

We consider a nondegenerate case of generic singularity when the limit cylinder of the rescaled mean curvature flow is R 3 × S 1 . We obtain a detailed description of a possibly small, but fixed, neighborhood of the singularity, up to (and including) the blowup time, and find that it is mean convex and the singularity is isolated. In the considered nondegenerate cases, we confirm the conjectures of mean convexity and isolation of singularities.