Circle patterns on singular surfaces
Abstract
Description
We consider ``hyperideal'' circle patterns, i.e. patterns of disks appearing in the definition of the Delaunay decomposition associated to a set of disjoint disks, possibly with cone singularities at the center of those disks. Hyperideal circle patterns are associated to hyperideal hyperbolic polyhedra. We describe the possible intersection angles and singular curvatures of those circle patterns, on Euclidean or hyperbolic surfaces with conical singularities. This is related to results on the dihedral angles of ideal or hyperideal hyperbolic polyhedra.
41 pages, 10 figures. v2: more complete statements, simpler proofs, intro rewritten to mention Delaunay decompositions
41 pages, 10 figures. v2: more complete statements, simpler proofs, intro rewritten to mention Delaunay decompositions