Because the scalar curvature under Ricci flow evolve by $$ \partial_t R=\Delta R+ 2|Ric|^2 $$ I treat it as heat equation with heat source . So, no matter the heat source is very hot or not , the scalar curvature will be positive everywhere on manifold ,if $\int _M R_{t=0}dV >0$. But this condition don't means the curvature is positive in everywhere at beginning . And not all manifold can be placed metric with positive curvature. So, on such manifold, the Ricci flow will evolve the manifold to unconnected parts if we suitably cut and mend the singularity. At last the different parts will evolve to manifold with non-negative curvature. So, in fact ,Ricci flow can be used as a way to cut manifold to non-negative curvature parts. And in the process, the manifold only can be placed metric with negative curvature will be decomposed (if there is such manifold) . So There is a way of classification manifold contained in Ricci flow. But as I know , there are only preliminary work of classify 4-manifold.
I just happen to think of this ,and my base is weak . So I don't know whether right this idea. Maybe , this is not a precise question , but I really curious about it .