4 problems

La Nave–Tian's conjecture. As $t\to\infty$,

Chen's conjecture. The quantity $R([\omega_0],\chi)$ is an invariant of the Kähler class $[\chi]$. This quantity measures how far the continuity path proceeds toward the constant s…

Partial-resolution continuation conjecture. The continuity equation can be solved on $M'$ for $t\in(0,T')$ with initial metric $\omega'_0$.

Finite-time metric convergence conjecture. As $t\to T$, $(M,\omega_t)$ converges in the GromovHausdorff topology to a compact metric space $(M_T,d_T)$ satisfying the following:…