UC Berkeley

We study the Ricci flow on Riemannian groupoids. We assume that these groupoids are closed and that the space of orbits is compact and connected. We derive maximum principles for groupoids and give some applications for immortal Ricci flow solutions on closed manifolds. We prove the short time existence and uniqueness of the Ricci flow on groupoids. We also define a F-functional and derive the corresponding results for steady breathers on these groupoids.