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arXiv · 2204.05253

Nonconvex ancient solutions to Curve Shortening Flow

Yongzhe Zhang·Connor Olson·Ilyas Khan·Sigurd Angenent
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Abstract

We construct an ancient solution to planar curve shortening. The solution is at all times compact and embedded. For $t\ll0$ it is approximated by the rotating Yin-Yang soliton, truncated at a finite angle $\alpha(t) = -t$, and closed off by a small copy of the Grim Reaper translating soliton.

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Yongzhe Zhang, Connor Olson, Ilyas Khan, Sigurd Angenent. 2022-04-11. Nonconvex ancient solutions to Curve Shortening Flow. https://arxiv.org/abs/2204.05253

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