2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143303In this paper we construct an example of a weakly complete maximal surface in the Lorentz-Minkowski space L^3, which is bounded by a hyperboloid. Moreover, all the singularities of our example are of lightlike type.12 pages, 2 figures. Revised version. To appear in Differ. Geom. ApplDifferential Geometry53C50 (Primary); 53C42, 53A10, 53B30 (Secondary)text