2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159742In this work, complete constant mean curvature 1 (CMC-1) surfaces in hyperbolic 3-space with total absolute curvature at most 4 pi are classified. This classification suggests that the Cohn-Vossen inequality can be sharpened for surfaces with odd numbers of ends, and a proof of this is given.19 pages, 5 figuresDifferential Geometry53A10; 53A35; 53A42text