The heat equation shrinks embedded plane curves to round points

M. Grayson

Type: Article

Publication Date: 1987-01-01

Citations: 1023

DOI: https://doi.org/10.4310/jdg/1214441371

Abstract

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 ∞

Locations

Journal of Differential Geometry - View - PDF

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