If g is a metric whose Ricci flow g (t) converges, one may ask if the same is true for metrics g that are small perturbations of g. We use maximal regularity theory and center manifold analysis to study flat and Ricci-flat metrics. We show that if g is flat, there is a unique exponentially-attractive center manifold at g consisting entirely of equilibria for the flow. Adding a continuity argument, we prove stability for any metric whose Ricci flow converges to a flat metric. We obtain a slightly weaker stability result for a Kahler-Einstein metric on a KS manifold.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.