Discrete conformal welding

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10 Scopus citations


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
Issue number3
StatePublished - 2004


  • Circle packing
  • Conformal welding
  • Quasicircle
  • Quasisymmetric map


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