2 problems

Optimality conjecture. The constant $m=\frac{2}{n+1}\left(\frac{n}{n+1}\right)^n$ is optimal for all Kähler manifolds $(X,\omega)$.

Self-repulsiveness conjecture. The regularized $\alpha$-energy $E_\alpha$ for smooth closed surfaces is self-repulsive with respect to $C^0$-topology if and only if $\alpha\leq -4$…