Disclaimer: I know close to nothing about differential geometry, only basics due to my early interest in general relativity when I was in high school almost 20 years ago. Therefore the present question would probably not be relevant for MathOverflow, and that's why I'm asking it here.
Suppose $(M,g)$ is a Riemannian manifold of dimension at least two. Under which hypotheses can one be sure that at least one point thereof has the same scalar curvature when a Ricci flow is performed during the whole process?
Many thanks in advance and sorry is this question ever turns out to make no sense.