Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159841We describe local similarities and global differences between minimal surfaces in Euclidean 3-space and constant mean curvature 1 surfaces in hyperbolic 3-space. We also describe how to solve global period problems for constant mean curvature 1 surfaces in hyperbolic 3-space, and we give an overview of recent results on these surfaces. We include computer graphics of a number of examples.Differential Geometry53A10; 53A35; 53A42Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean spacetext