Abstract

Let Σ_g be a closed orientable surface of genus g ≥ 2 and τ a graph on Σ_g with one vertex that lifts to a triangulation of the universal cover. We have shown before that the cross ratio parameter space C_τ associated with τ, which can be identified with the set of all pairs of a projective structure and a circle packing on it with nerve isotopic to τ, is homeomorphic to R^6g−6, and moreover that the forgetting map of C_τ to the space of projective structures is injective. Here we show that the composition of the forgetting map with the uniformization from C_τ to the Teichmüller space T_g is proper.

Keywords

circle packing, projective structure, uniformization, Teichmüller space

Mathematical Subject Classification

Primary: 57M27

Authors