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Sphere-preserving maps in inversive geometry

Authors: A. F. Beardon and D. Minda
Journal: Proc. Amer. Math. Soc. 130 (2002), 987-998
MSC (1991): Primary 30C35; Secondary 51F15
Published electronically: November 9, 2001
MathSciNet review: 1873771
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Abstract: We give an extensive discussion of sphere-preserving maps defined on subdomains of Euclidean $n$-space, and their relationship to Möbius maps and to the preservation of cross-ratios. In the case $n=2$ (the complex plane) we also relate these ideas to the solutions of certain functional equations.

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Additional Information

A. F. Beardon
Affiliation: Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, England

D. Minda
Affiliation: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025

Received by editor(s): February 29, 2000
Published electronically: November 9, 2001
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2001 American Mathematical Society