Let $M$ be a compact, smooth manifold and $\{g(t)\}$ be a family of Riemannian metrics on $M$ evolving under Ricci flow. Suppose the maximal existence time $T$ is finite. To what extent the following is true: there is a compact metric space $(X,d)$ such that as $t\rightarrow T$, $(M,g(t))$ converges to $(X,d)$ in Gromov Hausdorff topology?
It is not known that if maximal existence time of Ricci flow is finite then the diameter remains bounded. Hence the above question can not have positive answer in literature. I am wondering if some partial results are known, e.g. does diameter bound imply that the G-H limit exist?
