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https://doi.org/10.2140/pjm.2006.225.287
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 Uniformization |
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. https://doi.org/10.2140/pjm.2006.225.287 | 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 | URI: | http://scholarbank.nus.edu.sg/handle/10635/102985 | ISSN: | 00308730 | DOI: | 10.2140/pjm.2006.225.287 |
Appears in Collections: | Staff Publications |
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