Crane, Edward and Short, Ian
PDF (Accepted Manuscript)
- Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
|DOI (Digital Object Identifier) Link:||https://doi.org/10.1093/qmath/hap044|
|Google Scholar:||Look up in Google Scholar|
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|
|Academic Unit/Department:||Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
|Depositing User:||Ian Short|
|Date Deposited:||29 Jul 2010 11:56|
|Last Modified:||06 Oct 2016 06:38|
|Share this page:|
Download history for this item
These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.