# Classification of compact ancient solutions to the curve shortening flow

@article{Daskalopoulos2008ClassificationOC, title={Classification of compact ancient solutions to the curve shortening flow}, author={Panagiota Daskalopoulos and Richard S. Hamilton and Nata{\vs}a {\vS}e{\vs}um}, journal={arXiv: Differential Geometry}, year={2008} }

We consider an embedded convex ancient solution $\Gamma_t$ to the curve shortening flow in $\mathbb{R}^2$. We prove that there are only two possibilities: the family $\Gamma_t$ is either the family of contracting circles, which is a type I ancient solution, or the family of evolving Angenent ovals, which correspond to a type II ancient solution to the curve shortening flow. We also give a necessary and sufficient curvature condition for an embedded, closed ancient solution to the curve…

## 77 Citations

### Classification of Convex Ancient Solutions to Curve Shortening Flow on the Sphere

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### Peer Reviewed Title: Classification of Convex Ancient Solutions to Curve Shortening Flow on the Sphere Author:

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### Convergence of curve shortening flow to translating soliton

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### Convex ancient solutions to curve shortening flow

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We show that the only convex ancient solutions to curve shortening flow are the stationary lines, shrinking circles, Grim Reapers and Angenent ovals, completing the classification initiated by…

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