Inverse mean curvature flow and Ricci-pinched three-manifolds

Abstract

Let $(M,g)$ be a complete, connected, non-compact Riemannian three-manifold with non-negative Ricci curvature satisfying $Ric\ge \epsilon \mathrm{tr}(Ric)g$ for some $\epsilon >0$. 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.

Final version to appear in J. Reine Angew. Math

Cited by in corpus (1)

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