Classification of compact ancient solutions to the curve shortening flow

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dc.creatorDaskalopoulos, Panagiota
dc.creatorHamilton, Richard
dc.creatorSesum, Natasa
dc.date2008-06-10
dc.date.accessioned2026-07-07T09:43:40Z
dc.date.available2026-07-07T09:43:40Z
dc.descriptionWe consider an embedded convex ancient solution $Γ_t$ to the curve shortening flow in $\mathbb{R}^2$. We prove that there are only two possibilities: the family $Γ_t$ 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 shortening flow to be convex.
dc.identifierhttps://arxiv.org/abs/0806.1757
dc.identifierhttp://arxiv.org/abs/0806.1757
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162648
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject53C44
dc.titleClassification of compact ancient solutions to the curve shortening flow
dc.typetext

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