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arXiv · 2607.23879

Closed mean curvature flows with prescribed tangent flows

Jingwen Chen·Tang-Kai Lee·Ao Sun·Xinrui Zhao
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Abstract

Given an embedded shrinker $\Sigma$ in $\mathbb{R}^{n+1}$ that is either closed, asymptotically conical, or a Cartesian product of such a shrinker with $\mathbb{R}^k$, we construct a closed embedded mean curvature flow whose tangent flow at the first singularity is modeled on $\Sigma$. We also prescribe the first-order asymptotics of the tangent flow. This result is a consequence of a more general theorem that allows us to construct mean curvature flows with an additional force whose tangent flow and first-order asymptotics at the first singularity are prescribed.

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Jingwen Chen, Tang-Kai Lee, Ao Sun, Xinrui Zhao. 2026-07-26. Closed mean curvature flows with prescribed tangent flows. https://arxiv.org/abs/2607.23879

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