Title: The Yamabe flow on asymptotically Euclidean manifolds
Abstract: Introduced by Hamilton in 1988, the Yamabe flow on a compact manifold is now known to converge in most cases to a metric of constant scalar curvature. I will describe joint work with Gilles Carron and Yi Wang in which we prove that the Yamabe flow on an asymptotically Euclidean manifold converges to a scalar-flat metric if and only if the initial metric has Yamabe constant Y>0, and characterize the infinite-time behavior of the flow in the remaining cases when Y≤0.