2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66891We compute the flux of Killing fields through ends of constant mean curvature 1 in hyperbolic space, and we prove a result conjectured by Rossman, Umehara and Yamada : the flux matrix they have defined is equivalent to the flux of Killing fields. We next give a geometric description of embedded ends of finite total curvature. In particular, we show that we can define an axis for these ends that are asymptotic to a catenoid cousin. We also compute the flux of Killing fields through these ends, and we deduce some geometric properties and some analogies with minimal surfaces in Euclidean space.31 pages, 1 figure, submitted to Illinois Journal of MathematicsDifferential Geometry53A10 (Primary) 53A35, 53C42, 30F45 (Secondary)text