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Title: Circle packings on surfaces with projective structures and uniformization
Authors: Kojima, S.
Mizushima, S.
Tan, S.P. 
Keywords: Circle packing
Projective structure
Teichmüller space
Issue Date: Jun-2006
Citation: Kojima, S., Mizushima, S., Tan, S.P. (2006-06). Circle packings on surfaces with projective structures and uniformization. Pacific Journal of Mathematics 225 (2) : 287-300. ScholarBank@NUS Repository.
Abstract: Let Σg be a closed orientable surface of genus g ≥ 2 and a graph on Σg with one vertex that lifts to a triangulation of the universal cover. We have shown before that the cross ratio parameter space C{script}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{double-struck}6g-6, and moreover that the forgetting map of C{script}τ to the space of projective structures is injective. Here we show that the composition of the forgetting map with the uniformization from C{script}τ to the Teichmüller space T{script}g is proper.
Source Title: Pacific Journal of Mathematics
ISSN: 00308730
DOI: 10.2140/pjm.2006.225.287
Appears in Collections:Staff Publications

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