2009 DG-MP-PDE Seminar - 01

In this talk we present two stability results. Firstly we present a stability result for graphical, rotationally symmetric, translating solutions to mean curvature flow. There we obtain that for initial data that converge spatially at infinity to such a soliton, the flow converges for large times to that soliton, without imposing any decay rates. Secondly we discuss Ricci flow of initial metrics which are asymptotically Euclidean. For small perturbations of the metric of Euclidean space, we show that the Ricci harmonic map heat flow converges to Euclidean space for large times. We also investigate the convergence of the diffeomorphisms relating Ricci harmonic map heat flow to Ricci flow. The first result is joint work with J. Clutterbuck and O.C. Schnuerer, the second result is joint work with M. Simon and O.C. Schnuerer.