Geometry Workshop Obergurgl 2021

Canonical cell decompositions of decorated hyperbolic cusp surfaces, provided by the Epstein-Penner convex hull construction, have proven to be useful in the context of discrete conformal analysis and polyhedral realisation problems. This talk will give an overview of a generalisation to finite type hyperbolic surfaces, including a flip algorithm to compute such tessellations from an arbitrary initial triangulation of the surface.