2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74027We give a new proof that the completion of the Weil-Petersson metric on Teichmüller space is Gromov-hyperbolic if the surface is a five-times punctured sphere or a twice-punctured torus. Our methods make use of the synthetic geometry of the Weil-Petersson metric.11 pages. Revised version, to appear in "Spaces of Kleinian Groups", LMS Lecture Notes, Eds. Y.Minsky, M.Sakuma, C.SeriesDifferential Geometrytext