Crane, Edward and Short, Ian
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|DOI (Digital Object Identifier) Link:||http://doi.org/10.1093/qmath/hap044|
|Google Scholar:||Look up in Google Scholar|
We answer two questions of Beardon and Minda which arose from their study of the conformal symmetries of circular regions in the complex plane. We show that a configuration of closed balls in the N-sphere is determined up to Möbius transformations by the signed inversive distances between pairs of its elements, except when the boundaries of the balls have a point in common, and that a configuration of points in the N-sphere is determined up to Möbius transformations by the absolute cross-ratios of 4-tuples of its elements. The proofs use the hyperboloid model of hyperbolic (N + 1)-space.
|Item Type:||Journal Article|
|Copyright Holders:||2010 Oxford University Press|
|Academic Unit/Department:||Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
|Depositing User:||Ian Short|
|Date Deposited:||29 Jul 2010 11:56|
|Last Modified:||14 Aug 2016 03:40|
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