Circle packings on surfaces with projective structures and uniformization

Sadayoshi Kojima, Shigeru Mizushima, Ser Peow Tan
2006 Pacific Journal of Mathematics  
Let Σ g be a closed orientable surface of genus g ≥ 2 and τ a graph on Σ g with one vertex which lifts to a triangulation of the universal cover. We have shown 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. In this paper, we show
more » ... is paper, we show that the composition of the forgetting map with the uniformization from C τ to the Teichmüller space T g is proper. 2000 Mathematics Subject Classification. Primary 52C15; Secondary 30F99, 57M50.
doi:10.2140/pjm.2006.225.287 fatcat:w5rassowfzf6xkqpc6lydfkqnq