A collapsing ancient solution of mean curvature flow in $\mathbb{R}^3$

Theodora Bourni; Mat Langford; Giuseppe Tinaglia

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arXiv · 1705.06981

A collapsing ancient solution of mean curvature flow in $\mathbb{R}^3$

Theodora Bourni·Mat Langford·Giuseppe Tinaglia

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Abstract

We construct a compact, convex ancient solution of mean curvature flow in $\mathbb R^{n+1}$ with $O(1)\times O(n)$ symmetry that lies in a slab of width $π$. We provide detailed asymptotics for this solution and show that, up to rigid motions, it is the only compact, convex, $O(n)$-invariant ancient solution that lies in a slab of width $π$ and in no smaller slab.

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Theodora Bourni, Mat Langford, Giuseppe Tinaglia. 2017-09-30. A collapsing ancient solution of mean curvature flow in $\mathbb{R}^3$. https://arxiv.org/abs/1705.06981

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