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Convex ancient solutions to curve shortening flow


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 Daskalopoulos, Hamilton and Šešum and X.-J. Wang.

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Correspondence to Theodora Bourni.

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Communicated by N. Trudinger.

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Bourni, T., Langford, M. & Tinaglia, G. Convex ancient solutions to curve shortening flow. Calc. Var. 59, 133 (2020).

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Mathematics Subject Classification

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  • 35