Sphere-preserving maps in inversive geometry

Beardon, A.; Minda, D.

doi:10.1090/S0002-9939-01-06427-9

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.

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