2 problems

Lemniscate stability conjecture. As in the circle case, an analogous stability result should hold for the lemniscate under the free elastic flow.

Let $\mathcal M$ be a cone and let a closed curve on $\mathcal M$ be not homotopic to a point on $\mathcal M$. Elliott's conjecture. Under geodesic curvature flow, the curve will c…