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arXiv · 1909.02535

Codimension Bounds and Rigidity of Ancient Mean Curvature Flows by the Tangent Flow at $-\infty$

Douglas Stryker·Ao Sun
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Abstract

Motivated by the limiting behavior of an explicit class of compact ancient curve shortening flows, we prove codimension bounds for ancient mean curvature flows by their tangent flow at $-\infty$, generalizing a theorem for cylinders in [CM19b]. In the case of the $m$-covered circle, we apply this bound to prove a strong rigidity theorem. Furthermore, we extend this paradigm by showing that under the assumption of sufficiently rapid convergence, a compact ancient mean curvature flow is identical to its tangent flow at $-\infty$.

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Douglas Stryker, Ao Sun. 2019-09-05. Codimension Bounds and Rigidity of Ancient Mean Curvature Flows by the Tangent Flow at $-\infty$. https://arxiv.org/abs/1909.02535

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