Kähler–Ricci soliton convergence conjecture for pluriclosed flow on Fano surfaces

Let $(M^4,J)$ be a compact Fano surface admitting a Kähler–Ricci soliton $(\omega_{KRS},X)$. Let $\omega_0\in c_1$ be a Kähler metric invariant under the one-parameter subgroup $G_X$ generated by $\operatorname{Im}(X)$. Fano soliton convergence conjecture. The solution to normalized pluriclosed flow exists on $[0,\infty)$ and converges to a Kähler–Ricci soliton. The passage presents this as the expected analogue of the established Kähler–Ricci-flow result, with no resolution supplied.