On the dynamics of formation of generic singularities of mean curvature flow

We study formation of generic singularities under mean curvature flow by combining the different approaches and results, namely the techniques used by the author and the collaborators, where we obtained detailed information when the initial hypersurfaces are close to cylinders, and these results by Colding and Minicozzi, which included all the generic blowups. Here we choose to study the cases where the rescaled flow converges to the cylinder S-1 x R-3 , and we extend the region controlled by Colding and Minicozzi to find a finer description of a neighborhood of the singularity. (C)2022 Elsevier Inc. All rights reserved.

Automated summary

In this study, we examine the formation of generic singularities under mean curvature flow by combining different approaches and results. We obtained detailed information when the initial hypersurfaces are close to cylinders and also included all the generic blowups from the results by Colding and Minicozzi. We focused on the cases where the rescaled flow converges to the cylinder S-1 x R-3 and extended the region controlled by Colding and Minicozzi to provide a finer description of the singularity's neighborhood.