UNIFORMIZING SURFACES VIA DISCRETE HARMONIC MAPS

Toru Kajigaya, Ryokichi Tanaka

Research output: Contribution to journalArticlepeer-review

Abstract

We show that for any closed surface of genus greater than one and for any finite weighted graph filling the surface, there exists a hyperbolic metric which realizes the least Dirichlet energy harmonic embedding of the graph among a fixed homotopy class and all hyperbolic metrics on the surface. We give explicit examples of such hyperbolic surfaces as a refinement of the Nielsen realization problem for the mapping class groups.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2019 May 14

Keywords

  • Discrete harmonic maps
  • Finite weighted graphs
  • Hyperbolic surfaces
  • Weil-Petersson geometry of Teichmüller spaces

ASJC Scopus subject areas

  • General

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