2 problems

Domokos–Várkonyi approximation conjecture. For any centered convex body $K\subset\mathbb R^3$, $K$ can be uniformly approximated by monostable convex polyhedra if and only if…

Curvature-relaxed approximation conjecture. Theorem remains true if the condition that the principal curvatures of $\operatorname{bd}(K)$ at every equilibrium point of $K$ are stri…