Ricci flow of W^{2,2} metrics in four dimensions

Abstract: In this talk we construct solutions to Ricci de Turck flow in four dimensions on compact manifolds which are instantaneously smooth but whose initial values are (possibly) non-smooth Riemannian metrics whose components, in smooth coordinates, belong to $W^{2,2}$ and are bounded from above and below. A Ricci flow related solution is constructed whose initial value is isometric in a weak sense to the initial value of the Ricci de Turck solution. (joint work with Tobias Lamm)