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

DOI:
https://doi.org/10.1090/S0002-9939-01-06427-9

Published electronically:
November 9, 2001

MathSciNet review:
1873771

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Abstract | References | Similar Articles | Additional Information

Abstract: We give an extensive discussion of sphere-preserving maps defined on subdomains of Euclidean -space, and their relationship to Möbius maps and to the preservation of cross-ratios. In the case (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

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

DOI:
https://doi.org/10.1090/S0002-9939-01-06427-9

Received by editor(s):
February 29, 2000

Published electronically:
November 9, 2001

Communicated by:
Juha M. Heinonen

Article copyright:
© Copyright 2001
American Mathematical Society