2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65659We give a new and complete proof of Hamilton's injectivity radius estimate for sequences with bounded and almost nonnegative curvature operators, unbounded diameters, and bump-like origins. Such sequences arise in particular from dilations about a singularity of the Ricci flow on a 3-manifold.Differential Geometry53C20text