Topology of closed hypersurfaces of small entropy

Abstract

We use a weak mean curvature flow together with a surgery procedure to show that all closed hypersurfaces in ${ℝ}^4$ with entropy less than or equal to that of ${\mathbb{S}}^2\times ℝ$, the round cylinder in ${ℝ}^4$, are diffeomorphic to ${\mathbb{S}}^3$.