  Under suitable conditions near infinity and assuming boundedness of curvature
tensor, we prove a no breathers theorem in the spirit of Ivey-Perelman for some
noncompact Ricci flows. These include Ricci flows on asymptotically flat (AF)
manifolds with positive scalar curvature. Since the method for the compact case
faces a difficulty, the proof involves solving a new non-local elliptic
equation which is the Euler-Lagrange equation of a scaling invariant log
Sobolev inequality.
