Inverse mean curvature flow and Ricci-pinched three-manifolds

Gerhard Huisken, Thomas Koerber
Let (M,g) be a complete, connected, non-compact Riemannian three-manifold with non-negative Ricci curvature satisfying Ric≥εtr(Ric)g for some ε>0. In this note, we give a new proof based on inverse mean curvature flow that (M,g) is either flat or has non-Euclidean volume growth. In conjunction with results of J. Lott and of M.-C. Lee and P. Topping, this gives an alternative proof of a conjecture of R. Hamilton recently proven by A. Deruelle, F. Schulze, and M. Simon using Ricci flow.