Higher-dimensional bounded-diameter conjecture for Type I Ricci flows

Let $M$ be a compact manifold and $g(t)$, $t\in [0,T)$ be a smooth Ricci flow on $M$, which may become singular at $t=T$. A Ricci flow is Type I if, for some constant $C_I<+\infty$, its curvature tensor satisfies

$$|\operatorname{Rm}|\leq \frac{C_I}{T-t}$$

on $M\times [0,T)$. Higher-dimensional bounded-diameter conjecture. Possibly under the Type I condition, the diameter of $g(t)$ is uniformly bounded for every $0\leq t<T$. The paper proves the corresponding bounded-diameter result, together with a uniform bound on the total curvature, for compact three-dimensional manifolds. The conjecture asks whether the diameter conclusion remains valid in higher dimensions.