Parabolic geometric evolution systems such as the Ricci-flow and the mean curvature flow can be used to deform a given Riemannian manifold or a given submanifold of a Riemannian manifold into a simpler geometry that can be classified, as in the proof of the Poincare conjecture by Hamilton and Perelman. The lecture describes joint work with C. Sinetsrari and S. Brendle how mean curvature flow and other fully non-linear evolution systems can be combined with a surgery algorithm to deform and classify a natural class of hypersurfaces in Riemannian manifolds.