Circle packings on surfaces with projective structures and uniformization

• Autores: Sadayoshi Kojima, Shigeru Mizushima, Ser Peow Tan
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 225, Nº 2, 2006, págs. 287-300
• Idioma: inglés
• DOI: 10.2140/pjm.2006.225.287
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• Resumen

  • Let Sg be a closed orientable surface of genus g = 2 and t a graph on Sg with one vertex that lifts to a triangulation of the universal cover. We have shown before that the cross ratio parameter space Ct associated with t, which can be identified with the set of all pairs of a projective structure and a circle packing on it with nerve isotopic to t, is homeomorphic to R6g-6, and moreover that the forgetting map of Ct to the space of projective structures is injective. Here we show that the composition of the forgetting map with the uniformization from Ct to the Teichmüller space Tg is proper.