The heat equation shrinks embedded plane curves to round points

@article{Grayson1987TheHE,
  title={The heat equation shrinks embedded plane curves to round points},
  author={M. Grayson},
  journal={Journal of Differential Geometry},
  year={1987},
  volume={26},
  pages={285-314}
}
  • M. Grayson
  • Published 1987
  • Mathematics
  • Journal of Differential Geometry
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 lisse pour tout t, il converge vers un point quand t\T et sa forme limite quand t→T est un cercle rond, avec convergence dans norme C ∞ 
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