2 problems

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 $\alpha\leq -4$…

Let $[K_1]$ and $[K_2]$ be isotopy classes of knots, and let $[K_1\sharp K_2]$ be their composite isotopy class. For an isotopy class $[K]$, write $E^{(2)}_{\circ}([K])$ for the in…