2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210470We find complete hypersurfaces of constant curvature in hyperbolic space with a prescribed asymptotic boundary at infinity for a general class of (elliptic) curvature functions which includes the higher order mean curvatures and their curvature quotients.revised for publicationDifferential Geometry53C21 (Primary), 35J65, 58J32 (Secondary)text