2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78779We study the moduli space of euclidean structures with cone points on a surface, and describe a decomposition into cells each of which corresponds to a given combinatorial type of Delaunay tessellation. We use some of the ideas to study hyperbolic structures on three-dimensional manifolds27 pages, 1996 preprintGeometric TopologyMathematical PhysicsDifferential GeometryOptimization and Control52B10;52B70;57M50;81T40;68U05text