@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",
}