The Kähler–Ricci flow Gromov–Hausdorff convergence conjecture

Let $X$ be a smooth minimal model of general type, let $X_{can}$ be its canonical model, and let $g(t)$ be the solution of the normalized Kähler–Ricci flow

$$\frac{\partial g}{\partial t}=-\operatorname{Ric}(g)-g,\qquad g(0)=g_0.$$

Kähler–Ricci flow convergence conjecture. The metric spaces $(X,g(t))$ converge to the metric completion $(X_{can},g_\infty)$ in Gromov–Hausdorff topology as $t\to\infty$. This is presented as a well-known conjecture; the preceding proposition establishes smooth convergence away from the exceptional locus, while the global metric convergence remains open.