Inverse mean curvature flow and Ricci-pinched three-manifolds

Let (M,g) be a complete, connected, noncompact Riemannian three-manifold with nonnegative Ricci curvature. R. Hamilton has conjectured that if the largest eigenvalue of the Ricci curvature of (M,g) is less than the product of its smallest eigenvalue and a universal constant, then (M,g) is flat. This conjecture has recently been confirmed by A. Deruelle, F. Schulze and M. Simon using Ricci flow. In this lecture, I will present a short new proof of R. Hamilton's conjecture based on inverse

mean curvature flow. This is joint work with Gerhard Huisken.