Suppose I have a Ricci flow $(M, g(t))$ on $[0, T)$ can it develop a singularity if the metrics $g(t)$ are uniformly bounded?
i.e $C^{-1}g(0)\leq g(t) \leq Cg(0)$ for all $t\in [0,T)$.
In the Kahler case, I think if you can control the metric, you can control the curvature and then by Shi's theorem you can extend the flow past time $T$, but is there similar statement in the Riemannian case? If not, is there a counterexample?