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Relative Riemann mapping criteria and hyperbolic convexity

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

In: Proceedings of the American Mathematical Society, Vol. 140, No. 7, S 0002-9939(2011)11096-7, 07.2012, p. 2375-2382.

Research output: Contribution to journalArticle

Harvard

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

APA

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

Vancouver

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

Author

Crane, ET. / Relative Riemann mapping criteria and hyperbolic convexity. In: Proceedings of the American Mathematical Society. 2012 ; Vol. 140, No. 7. pp. 2375-2382.

Bibtex

@article{64aabc1a9e8d4273b95b7c678b092c20,
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",
year = "2012",
month = "7",
doi = "10.1090/S0002-9939-2011-11096-7",
language = "English",
volume = "140",
pages = "2375--2382",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "7",

}

RIS - suitable for import to EndNote

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AU - Crane, ET

PY - 2012/7

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N2 - 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 Jørgensen. We discuss the close relationship of our criterion to two generalizations of Jørgensen'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.

AB - 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 Jørgensen. We discuss the close relationship of our criterion to two generalizations of Jørgensen'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.

KW - Riemann mapping

KW - circle domains

KW - hyperbolic convexity

KW - conformal reflection

KW - quasidiscs

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DO - 10.1090/S0002-9939-2011-11096-7

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EP - 2382

JO - Proceedings of the American Mathematical Society

T2 - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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ER -