Classification of noncollapsed translators in ℝ⁴

2021/05/28 by Kyeongsu Choi, Choi, Kyeongsu, Robert Haslhofer +3
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2105.13819

openalex publication_date 2021/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we classify all noncollapsed singularity models for the mean curvature flow of 3-dimensional hypersurfaces in ℝ⁴ or more generally in 4-manifolds. Specifically, we prove that every noncollapsed translating hypersurface in ℝ⁴ is either ℝ×2d-bowl, or a 3d round bowl, or belongs to the one-parameter family of 3d oval bowls constructed by Hoffman-Ilmanen-Martin-White.

Related

• Classification of ancient noncollapsed flows in ℝ⁴
• Mean curvature flow through singularities
• Singularity models of pinched solutions of mean curvature flow in higher codimension
• Translation hypersurfaces with constant curvature in 4-dimensional isotropic space
• Hearing the shape of ancient noncollapsed flows in ℝ⁴