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Intrinsic circle domains

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)65-84
Number of pages20
JournalConformal Geometry and Dynamics
Volume18
Early online date1 May 2014
DOIs
DateE-pub ahead of print - 1 May 2014
DatePublished (current) - 1 May 2014

Abstract

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.

    Research areas

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

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  • Intrinsic circle domains

    Rights statement: First published in Conformal Geometry and Dynamics, Volume 18, 2014, published by the American Mathematical Society

    Submitted manuscript, 897 KB, PDF document

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