2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33366We prove that the space of smooth initial data and the set of smooth solutions of the Liouville equation are homeomorphic.LaTeX2e, 21 pages, no figures, submitted for publicationDifferential GeometryTopology of the set of smooth solutions to the Liouville equationtext