5 problems

Let $(X,\omega_0)$ be a compact Kähler manifold, and let…

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 $\alpha\leq -4$…

Let $K$ be a knot, let $N_\varepsilon(K)$ be its $\varepsilon$-tubular neighbourhood, and let $\lambda$ and $\lambda'$ be real parameters. Expand…

Let $M$ be an $m$-dimensional compact orientable submanifold of $\mathbb R^n$, let $\lambda$ be real, and define … where…