2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154941This note provides an alternative proof of a result of Labourie. We show that the two complements of the convex core of a three dimensional quasi-fuchsian hyperbolic manifold may be foliated by embedded hypersurfaces of constant Gaussian curvature.Differential Geometry53C12; 35J60; 37F30; 51M10text