Abstract
In this paper we classify convex compact ancient solutions to the affine curve shortening flow, namely, any convex compact ancient solution to the affine curve shortening flow must be a shrinking ellipse. The method combines a rescaling argument inspired by Wang (Ann. Math., 173(1):1185–1239, 2011), affine invariance of the equation, and monotonicity of the affine isoperimetric ratio. It also provides a new simple proof for the corresponding classification result to the higher-dimensional affine normal flow.
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