Inverse mean curvature flow and Ricci-pinched three-manifolds

Abstract Let (M, g) (M, g) be a noncompact, connected, complete Riemannian three-manifold with nonnegative Ricci curvature satisfying Ric ≥ ε ⁢ tr ⁡ (Ric) ⁢ g Ric (Ric) g for some ε > 0 >0. In this note, we give a new proof based on inverse mean curvature flow that (M, g) (M, g) is either flat or has non-Euclidean volume growth. In conjunction with the work of J. Lott On 3-manifolds with pointwise pinched nonnegative Ricci curvature, Math. Ann. 388 (2024), 3, 2787–2806 and of M. -C. Lee and P. Topping Three-manifolds with non-negatively pinched Ricci curvature, preprint (2022), https: //arxiv. org/abs/2204. 00504, this gives an alternative proof of a conjecture of R. Hamilton recently proven by A. Deruelle, F. Schulze, and M. Simon Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds, preprint (2022), https: //arxiv. org/abs/2203. 15313 using Ricci flow.