  We study Ricci flows on $R^n$, $n\ge 3$, that evolve from asymptotically flat
initial data. Under mild conditions on the initial data, we show that the flow
exists and remains asymptotically flat for an interval of time. The mass is
constant in time along the flow. We then specialize to the case of rotationally
symmetric, asymptotically flat initial data containing no embedded minimal
hyperspheres. We show that in this case the flow is immortal, remains
asymptotically flat, never develops a minimal hypersphere, and converges to
flat Euclidean space as the time diverges to infinity. We discuss the behaviour
of quasi-local mass under the flow, and relate this to a conjecture in string
theory.
