## Intrinsic circle domains

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- by Edward Crane PDF
- Conform. Geom. Dyn.
**18**(2014), 65-84 Request permission

## Abstract:

Using quasiconformal mappings, we prove that any Riemann surface of finite connectivity and finite genus is conformally equivalent to an intrinsic circle domain $\Omega$ in a compact Riemann surface $S$. This means that each connected component $B$ of $S\setminus \Omega$ is either a point or a closed geometric disc with respect to the complete constant curvature conformal metric of the Riemann surface $(\Omega \cup B)$. Moreover, the pair $(\Omega , S)$ 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.## References

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## Additional Information

**Edward Crane**- Affiliation: Heilbronn Institute for Mathematical Research, School of Mathematics, University of Bristol, BS8 1TW, United Kingdom
- Email: edward.crane@bristol.ac.uk
- Received by editor(s): March 27, 2013
- Published electronically: May 1, 2014
- © Copyright 2014 American Mathematical Society
- Journal: Conform. Geom. Dyn.
**18**(2014), 65-84 - MSC (2010): Primary 30C20; Secondary 30F45, 30C30, 52C26
- DOI: https://doi.org/10.1090/S1088-4173-2014-00262-8
- MathSciNet review: 3199397