Classification of noncollapsed translators in ${\mathbb{R}}^4$

Abstract

In this paper, we classify all noncollapsed singularity models for the mean curvature flow of 3-dimensional hypersurfaces in ${\mathbb{R}}^4$ or more generally in $4$-manifolds. Specifically, we prove that every noncollapsed translating hypersurface in ${\mathbb{R}}^4$ is either $\mathbb{R}\times$2d-bowl, or a 3d round bowl, or belongs to the one-parameter family of 3d oval bowls constructed by Hoffman-Ilmanen-Martin-White.

arXiv comment98 pages