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arXiv · 2608.11011

Ancient mean curvature flow asymptotic to Simons cone

Junyoung Park
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Abstract

In this paper, we prove that a smooth, properly embedded ancient mean curvature flow that is asymptotic to $O(n)\times O(n)$ symmetric Simons cone for $n \geq 5$, and lies on one side of the cone has to have a unique asymptotics in the parabolic region. When additionally assuming mean convexity, we upgrade unique asymptotics to full uniqueness, and show that such flow has to be a stationary flow given by one of the leaves of the Hardt-Simon foliation.

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Junyoung Park. 2026-08-11. Ancient mean curvature flow asymptotic to Simons cone. https://arxiv.org/abs/2608.11011

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