Uniqueness of tangent flows at infinity for finite-entropy shortening
curves
Uniqueness of tangent flows at infinity for finite-entropy shortening
curves
In this paper, we prove that an ancient smooth curve shortening flow with finite-entropy embedded in $\mathbb{R}^2$ has a unique tangent flow at infinity. To this end, we show that its rescaled flows backwardly converge to a line with multiplity $m\geq 3$ exponentially fast in any compact region, unless the …