Mean curvature flow with generic low-entropy initial data II

TL;DR

This paper proves that the mean curvature flow of generic low-entropy hypersurfaces in dimensions 4 to 6 develops only typical singularities, advancing understanding of geometric evolution in higher dimensions.

Contribution

It establishes that under certain entropy conditions, the mean curvature flow in specific dimensions encounters only generic singularities, extending previous results to higher dimensions.

Findings

Flow encounters only generic singularities in specified dimensions.

Results apply to hypersurfaces with entropy below certain thresholds.

Advances understanding of singularity formation in geometric flows.

Abstract

We prove that the mean curvature flow of a generic closed embedded hypersurface in $\mathbb{R}^4$ or $\mathbb{R}^5$ with entropy $\leq 2$, or with entropy $\leq \lambda(\mathbb{S}^1)$ if in $\mathbb{R}^6$, encounters only generic singularities.