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

ET Crane, I Short

Research output: Contribution to journalArticle (Academic Journal)peer-review

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.
Translated title of the contributionRigidity of coonfigurations of balls and points in the N-sphere
Original languageEnglish
Pages (from-to)351 - 362
Number of pages12
JournalQuarterly Journal of Mathematics
Volume62
Issue number2
Early online date29 Jan 2010
DOIs
Publication statusPublished - Jun 2011

Bibliographical note

Publisher: Oxford University Press

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