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Rigidity of configurations of balls and points in the N-sphere

Crane, Edward and Short, Ian (2011). Rigidity of configurations of balls and points in the N-sphere. The Quarterly Journal of Mathematics, 62(2) pp. 351–362.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1093/qmath/hap044
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Abstract

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
ISSN: 1464-3847
Academic Unit/Department: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 22464
Depositing User: Ian Short
Date Deposited: 29 Jul 2010 11:56
Last Modified: 06 Oct 2016 06:38
URI: http://oro.open.ac.uk/id/eprint/22464
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