2001/02/22 by Karsten Große-Brauckmann, Karsten Grosse-Brauckmann, Robert B Kusner +6
Mathematics · #53A10 (Primary) 58D10 #53C42 (Secondary) #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53A10 #msc:53C42 #msc:58D10
paper · pdf · doi:10.48550/arxiv.math/0102183
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. Math
openalex publication_date 2001/02/22 · arxiv created 2003/04/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In 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.