3 problems

Let $M$ be a compact LCK complex surface with proper potential, and let $\widetilde M$ be its Kähler $\mathbb Z$-covering. The metric-completion conjecture. The metric completion o…

Let $M$ be a compact nilmanifold admitting a locally conformally Kähler (LCK) structure, and let $H(n)$ be the generalized Heisenberg group. Structure conjecture. Up to covering,…

Let $M$ be a compact locally conformally Kähler (LCK) manifold with automorphic potential, meaning that $M$ admits a Kähler covering with an automorphic potential. Monodromy conjec…