3 problems

Compactness and degeneration conjecture. If $V_i\to V\in(\underline V,+\infty)$, then there exists a sequence $\sigma_i\in PSL(2,\mathbf{C})$ such that

Large-volume limit conjecture. The large-volume limit, namely the Cheeger–Gromov limit based at $p_j$, converges to one of the solutions of Chen–Hastings–McLeod–Yang.

Let $M$ be a compact projective manifold with a Kähler metric $\omega_0\in q c_1(L')$, where $L'$ is a line bundle and $q$ is a positive rational number. Consider the family of equ…