B02 Geometric evolution equations

Hamilton’s Ricci flow is a geometric evolution equation on the space of Riemannian metrics of a smooth manifold. In a first subproject we would like to show a differentiable stability result for noncollapsed converging sequences of Riemannian manifolds with nonnegative sectional curvature, generalising Perelman’s topological stability. In a second subproject, next to classifying homogeneous Ricci solitons on non-compact homogeneous spaces, we would like to prove the dynamical Alekseevskii conjecture. Finally, in a third subproject we would like to find new Ricci flow invariant curvature conditions, a starting point for introducing a Ricci flow with surgery in higher dimensions.