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