The classical Bonnet-Myers theorem in differential geometry states that a Riemannian manifold whose Ricci curvature is greater or equal to one everywhere has to be compact. A natural question is if the condition on the Ricci curvature can be relaxed such that it still yields compactness. A conjecture of Hamilton states that this should hold in 3 dimensions if the Ricci tensor is uniformly pinched. We will discuss the motivation and a recent proof of this conjecture and how this is related to initial stability questions for the Ricci flow. This is joint work with A. Deruelle (Paris) and M. Simon (Magdeburg).