The Kähler–Ricci flow convergence conjecture for smooth minimal models

Let $X$ be a smooth Kähler manifold with nef canonical bundle, and let $g_0$ be any initial Kähler metric on $X$. Let $g(t)$ be the solution of the unnormalized Kähler–Ricci flow. Kähler–Ricci flow convergence conjecture. The metrics $g(t)$ should have uniformly bounded diameter and scalar curvature for all time. Furthermore, $(X,g(t))$ should converge in the Gromov–Hausdorff topology to a unique compact metric space $(\mathcal{Z},d_{\mathcal{Z}})$ homeomorphic to the canonical model $X_{can}$. The conjecture concerns uniqueness and geometric convergence of long-time Kähler–Ricci flows on smooth minimal models; the paper notes that subsequential Gromov–Hausdorff limits can be extracted, while uniqueness requires more delicate analysis and remains open.