2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77365We show that any compact orientable hyperbolic 3-cone-manifold with cone angle at most πcan be continuously deformed to a complete hyperbolic manifold homeomorphic to the complement of the singularity. This together with the local rigidity by Hodgson and Kerckhoff implies the global rigidity for compact orientable hyperbolic 3-cone-manifolds under the same angle assumption.to appear in J. Differential GeomGeometric TopologyDifferential Geometry57M50(Primary), 30F40(Secondary)text