Intrinsic circle domains

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Using quasiconformal mappings, we prove that any Riemann surface of finite connectivity and finite genus is conformally equivalent to an intrinsic circle domain U in a compact Riemann surface S. This means that each connected component B of S\U is either a point or a closed geometric disc with respect to the complete constant curvature conformal metric of the Riemann surface U union B. Moreover, the pair (U, S) is unique up to conformal isomorphisms. We give a generalization to countably infinite connectivity. Finally, we show how one can compute numerical approximations to intrinsic circle domains using circle packings and conformal welding.
Original languageEnglish
Pages (from-to)65-84
Number of pages20
JournalConformal Geometry and Dynamics
Early online date1 May 2014
Publication statusPublished - 1 May 2014


  • circle domains
  • hyperbolic metric
  • circle packing
  • conformal welding


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