2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60995In 1841, Delaunay constructed the embedded surfaces of revolution with constant mean curvature (CMC); these unduloids have genus zero and are now known to be the only embedded CMC surfaces with two ends and finite genus. Here, we construct the complete family of embedded CMC surfaces with three ends and genus zero; they are classified using their asymptotic necksizes. We work in a class slightly more general than embedded surfaces, namely immersed surfaces which bound an immersed three-manifold, as introduced by Alexandrov.LaTeX, 22 pages, 2 figures (8 ps files); full version of our announcement math.DG/9903101; final version (minor revisions) to appear in Crelle's J. reine angew. MathDifferential Geometry53A10 (Primary) 58D10, 53C42 (Secondary)text