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
View on Springer
32 Citations
Highly Influential Citations
6
Background Citations
13
Methods Citations
2
Results Citations
2

32 Citations

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    Acta Mathematica Sinica, English Series
  • 2021
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Curve shortening flow in a 3-dimensional pseudohermitian manifold

  • Shujing PanJun Sun
  • Mathematics
    Calculus of Variations and Partial Differential Equations
  • 2021
In this paper, we introduce a curve shortening flow in a 3-dimensional pseudohermitian manifold with vanishing torsion. The flow preserves the Legendrian condition and decreases the length of curves.…

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References

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Curve shortening makes convex curves circular

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 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 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) est…

An isoperimetric inequality with applications to curve shortening

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 ZΛgradient…

Shortening embedded curves