@article{9ae271b2b93e49138b962a023d8c97fa,
title = "Rigidity of configurations of balls and points in the N-sphere",
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 Mbius 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 Mbius transformations by the absolute cross-ratios of 4-tuples of its elements. The proofs use the hyperboloid model of hyperbolic (N 1)-space.",
author = "ET Crane and I Short",
note = "Publisher: Oxford University Press",
year = "2011",
month = "6",
doi = "10.1093/qmath/hap044",
language = "English",
volume = "62",
pages = "351 -- 362",
journal = "Quarterly Journal of Mathematics",
issn = "0033-5606",
publisher = "Oxford University Press",
number = "2",
}