Circle packings on surfaces with projective structures and uniformization

Sadayoshi Kojima, Shigeru Mizushima, Ser Peow Tan

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)287-300
Number of pages14
JournalPacific Journal of Mathematics
Volume225
Issue number2
DOIs
Publication statusPublished - 2006 Jun 1
Externally publishedYes

Fingerprint

Projective Structure
Circle packing
Uniformization
Cross ratio
Universal Cover
Nerve
Homeomorphic
Injective
Triangulation
Parameter Space
Genus
Closed
Graph in graph theory
Vertex of a graph

Keywords

  • Circle packing
  • Projective structure
  • Teichmüller space
  • Uniformization

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Circle packings on surfaces with projective structures and uniformization. / Kojima, Sadayoshi; Mizushima, Shigeru; Tan, Ser Peow.

In: Pacific Journal of Mathematics, Vol. 225, No. 2, 01.06.2006, p. 287-300.

Research output: Contribution to journalArticle

Kojima, Sadayoshi ; Mizushima, Shigeru ; Tan, Ser Peow. / Circle packings on surfaces with projective structures and uniformization. In: Pacific Journal of Mathematics. 2006 ; Vol. 225, No. 2. pp. 287-300.
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