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

  title={The shape of a figure-eight under the curve shortening flow},
  author={M. Grayson},
  journal={Inventiones mathematicae},
  • M. Grayson
  • Published 1 February 1989
  • Mathematics
  • Inventiones mathematicae

Curve shortening flow on singular Riemann surfaces

In this paper, we study curve shortening flow on Riemann surfaces with singular metrics. It turns out that this flow is governed by a degenerate quasilinear parabolic equation. Under natural

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In Euclidean geometry, the shortest distance between two points is a straight line. Chern made a conjecture (cf. [10]) in 1977 that an affine maximal graph of a smooth, locally uniformly convex

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Legendrian curve shortening flow in R 3

This gives a partial answer to a conjecture of Grayson [12], which states that all figure-eight curves with zero signed area should shrink to a point under curve shortening flow. In particular, our

Singularities of the Curve Shortening Flow in a Riemannian Manifold

  • Shuxia Pan
  • Mathematics
    Acta Mathematica Sinica, English Series
  • 2021
In this paper, the curve shortening flow in a general Riemannian manifold is studied, Altschuler’s results about the flow for space curves are generalized. For any n-dimensional (n ≥ 2) Riemannian

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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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

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