## Sphere-preserving maps in inversive geometry

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- by A. F. Beardon and D. Minda
- Proc. Amer. Math. Soc.
**130**(2002), 987-998 - DOI: https://doi.org/10.1090/S0002-9939-01-06427-9
- Published electronically: November 9, 2001
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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.## References

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## Bibliographic Information

**A. F. Beardon**- Affiliation: Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, England
- Email: A.F.Beardon@dpmms.cam.ac.uk
**D. Minda**- Affiliation: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025
- Email: David.Minda@math.uc.edu
- Received by editor(s): February 29, 2000
- Published electronically: November 9, 2001
- Communicated by: Juha M. Heinonen
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**130**(2002), 987-998 - MSC (1991): Primary 30C35; Secondary 51F15
- DOI: https://doi.org/10.1090/S0002-9939-01-06427-9
- MathSciNet review: 1873771