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Publication - Dr Edward Crane

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

    Citation

    Crane, E & Short, I, 2011, ‘Rigidity of configurations of balls and points in the N-sphere’. Quarterly Journal of Mathematics, vol 62., pp. 351 - 362

    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.

    Full details in the University publications repository