2 problems

Let $\Omega(t)$ be the evolving set with boundary parametrized by $x(t,\xi)$, and let the optimal control be the normal velocity control acting along this boundary. Denote the curv…

Let $\Gamma$ be a generic plane curve evolving under the curve-shortening flow. Denote by $n_U(t)$ the number of critical points of its radial function relative to the fixed point…