Discrete conformal welding

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

Classically the process of conformal welding played a key role in the development of Teichmüller theory and quasiconformal maps. More recently, it has gained attention from physicists as the mechanism for switching between two models of the Universal Teichmüller Space, which is becoming increasingly important in string theory. We develop a geometric method for constructing conformal weldings using circle packings. We consider weldings created by bilipschitz, quasisymmetric, and locally quasisymmetric identification maps and exhibit several computer-generated examples. This provides the first method for computing these weldings.

Original languageEnglish
Pages (from-to)765-804
Number of pages40
JournalIndiana University Mathematics Journal
Volume53
Issue number3
DOIs
StatePublished - 2004

Keywords

  • Circle packing
  • Conformal welding
  • Quasicircle
  • Quasisymmetric map

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