Closed mean curvature flows with asymptotically conical singularities

In this paper, we prove that for any asymptotically conical self-shrinker, there exists a closed hypersurface such that the mean curvature flow starting from it develops a singularity modeled on the given shrinker. The main technique is the Wa\. zewski box argument, used by Stolarski Sto in the proof of the corresponding theorem in the Ricci flow case.