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

Research output: Contribution to journalArticle

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Rigidity of configurations of balls and points in the N-sphere. / Crane, ET; Short, I.

In: Quarterly Journal of Mathematics, Vol. 62, No. 2, 06.2011, p. 351 - 362.

Research output: Contribution to journalArticle

Harvard

Crane, ET & Short, I 2011, 'Rigidity of configurations of balls and points in the N-sphere' Quarterly Journal of Mathematics, vol. 62, no. 2, pp. 351 - 362. https://doi.org/10.1093/qmath/hap044

APA

Crane, ET., & Short, I. (2011). Rigidity of configurations of balls and points in the N-sphere. Quarterly Journal of Mathematics, 62(2), 351 - 362. https://doi.org/10.1093/qmath/hap044

Vancouver

Crane ET, Short I. Rigidity of configurations of balls and points in the N-sphere. Quarterly Journal of Mathematics. 2011 Jun;62(2):351 - 362. https://doi.org/10.1093/qmath/hap044

Author

Crane, ET ; Short, I. / Rigidity of configurations of balls and points in the N-sphere. In: Quarterly Journal of Mathematics. 2011 ; Vol. 62, No. 2. pp. 351 - 362.

Bibtex

@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",

}

RIS - suitable for import to EndNote

TY - JOUR

T1 - Rigidity of configurations of balls and points in the N-sphere

AU - Crane, ET

AU - Short, I

N1 - Publisher: Oxford University Press

PY - 2011/6

Y1 - 2011/6

N2 - 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.

AB - 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.

U2 - 10.1093/qmath/hap044

DO - 10.1093/qmath/hap044

M3 - Article

VL - 62

SP - 351

EP - 362

JO - Quarterly Journal of Mathematics

T2 - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

SN - 0033-5606

IS - 2

ER -