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A nonexistence result for rotating mean curvature flows in $\mathbb{R}^{4}$ (2208.14280v2)
Published 30 Aug 2022 in math.DG and math.AP
Abstract: Some worrisome potential singularity models for the mean curvature flow are rotating ancient flows, i.e. ancient flows whose tangent flow at $-\infty$ is a cylinder $\mathbb{R}k\times S{n-k}$ and that are rotating within the $\mathbb{R}k$-factor. We note that while the $\mathbb{R}k$-factor, i.e. the axis of the cylinder, is unique by the fundamental work of Colding-Minicozzi, the uniqueness of tangent flows by itself does not provide any information about rotations within the $\mathbb{R}k$-factor. In the present paper, we rule out rotating ancient flows among all ancient noncollapsed flows in $\mathbb{R}4$.