2009/10/29 by Filippo Morabito, Morabito, Filippo, M. Magdalena Rodríguez +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.0910.5676
openalex publication_date 2009/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given k>=2, we construct a (2k-2)-parameter family of properly embedded minimal surfaces in H2 x R invariant by a vertical translation T, called Saddle Towers, which have total intrinsic curvature 4 pi(1-k), genus zero and 2k vertical Scherk-type ends in the quotient by T. As limits of those Saddle Towers, we obtain Jenkins-Serrin graphs over ideal polygonal domains (with total intrinsic curvature 2 pi(1-k)); we also get properly embedded minimal surfaces which are symmetric with respect to a horizontal slice and have total intrinsic curvature 4 pi(1-k), genus zero and k vertical planar ends.