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In this paper, we classify all noncollapsed singularity models for the meancurvature flow of 3-dimensional hypersurfaces in $\mathbb{R}^4$ or moregenerally in $4$-manifolds. Specifically, we prove that every noncollapsedtranslating 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 bowlsconstructed by Hoffman-Ilmanen-Martin-White.

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