Research output: Contribution to journal › Article

**Relative Riemann mapping criteria and hyperbolic convexity.** / Crane, ET.

Research output: Contribution to journal › Article

Crane, ET 2012, 'Relative Riemann mapping criteria and hyperbolic convexity' *Proceedings of the American Mathematical Society*, vol. 140, no. 7, S 0002-9939(2011)11096-7, pp. 2375-2382. https://doi.org/10.1090/S0002-9939-2011-11096-7

Crane, ET. (2012). Relative Riemann mapping criteria and hyperbolic convexity. *Proceedings of the American Mathematical Society*, *140*(7), 2375-2382. [S 0002-9939(2011)11096-7]. https://doi.org/10.1090/S0002-9939-2011-11096-7

Crane ET. Relative Riemann mapping criteria and hyperbolic convexity. Proceedings of the American Mathematical Society. 2012 Jul;140(7):2375-2382. S 0002-9939(2011)11096-7. https://doi.org/10.1090/S0002-9939-2011-11096-7

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title = "Relative Riemann mapping criteria and hyperbolic convexity",

abstract = "Let be a simply-connected Riemann surface with a simply-connected subdomain . We give a criterion in terms of conformal reflections to determine whether can be embedded in the complex plane so that is mapped onto a disc. If it can, then is convex with respect to the hyperbolic metric of , by a theorem of J{\o}rgensen. We discuss the close relationship of our criterion to two generalizations of J{\o}rgensen's theorem by Minda and Solynin. We generalize our criterion to the quasiconformal setting and also give a criterion for the multiply-connected case, where an embedding is sought that maps a given subdomain onto a circle domain.",

keywords = "Riemann mapping, circle domains, hyperbolic convexity, conformal reflection, quasidiscs",

author = "ET Crane",

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KW - Riemann mapping

KW - circle domains

KW - hyperbolic convexity

KW - conformal reflection

KW - quasidiscs

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