4 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.

Unimodality conjecture. There is a critical volume $V_c\in(\underline V,+\infty)$ such that $\lambda$ is strictly increasing on $(\underline V,V_c]$ from $0$ to $\lambda_c$, and st…

Uniqueness conjecture. For any $V\in(\underline V,+\infty)$, $\sharp\big(\mathfrak{M}_{EB}(L,\tau;\bm\phi,V)\big)=1$ for stable $\bm\phi$, while