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Classification of noncollapsed translators in $\mathbb{R}^4$ (2105.13819v2)
Published 28 May 2021 in math.DG and math.AP
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.