Weakly Circle-Preserving Maps in Inversive Geometry

Joel C. Gibbons; Yusheng Luo

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arXiv · 1308.1752

Weakly Circle-Preserving Maps in Inversive Geometry

Joel C. Gibbons·Yusheng Luo

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Abstract

Let S^n be the standard n-sphere embedded in R^{n+1}. A mapping T: S^n \to S^n, not assumed continuous or even measurable, nor injective, is called weakly circle-preserving if the image of any circle under T is contained in some circle in the range space S^n. The main result of this paper shows that any weakly circle-preserving map satisfying a very mild condition on its range T(S^n) must be a Mobius transformation.

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Joel C. Gibbons, Yusheng Luo. 2013-08-08. Weakly Circle-Preserving Maps in Inversive Geometry. https://arxiv.org/abs/1308.1752

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