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 S¹×R³, and we extend the region controlled by Colding and Minicozzi to find a finer description of a neighborhood of the singularity.