The shape of a figure-eight under the curve shortening flow

@article{Grayson1989TheSO,
  title={The shape of a figure-eight under the curve shortening flow},
  author={M. Grayson},
  journal={Inventiones mathematicae},
  year={1989},
  volume={96},
  pages={177-180}
}
  • M. Grayson
  • Published 1 February 1989
  • Mathematics
  • Inventiones mathematicae
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References

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A stable manifold theorem for the curve shortening equation
On presente une famille de solutions homothetiques de l'equation pour une courbe planaire ∂X/∂τ=KN et on demontre l'existence de varietes non lineaires stables et instables autour de telles solutions
The heat equation shrinks embedded plane curves to round points
Soit C(•,0):S 1 →R 2 une courbe lisse plongee dans le plan. Alors C:S 1 ×[0,T)→R 2 existe en satisfaisant δC/δt=K•N, ou K est la courbure de C, et N est son vecteur unite normal entrant. C(•,t) estExpand
The heat equation shrinking convex plane curves
Soient M et M' des varietes de Riemann et F:M→M' une application reguliere. Si M est une courbe convexe plongee dans le plan R 2 , l'equation de la chaleur contracte M a un point
The normalized curve shortening flow and homothetic solutions
The curve shortening problem, by now widely known, is to understand the evolution of regular closed curves γ: R/Z -> M moving according to the curvature normal vector: dy/dt = kN = -"the ZΛgradientExpand
Curve shortening makes convex curves circular