Legendrian curve shortening flow in $\mathbb{R}^3$
Legendrian curve shortening flow in $\mathbb{R}^3$
Motivated by Legendrian curve shortening flows in $\mathbb{R}^{3}$, we study the curve shortening flow of figure-eight curves in the plane. We show that, under some symmetry and curvature conditions, a figure-eight curve will shrink to a point at the first singular time.