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arXiv · 1008.3250

A Möbius Characterization of Metric Spheres

Thomas Foertsch·Viktor Schroeder
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Abstract

In this paper we characterize compact extended Ptolemy metric spaces with many circles up to Möbius equivalence. This characterization yields a Möbius characterization of the $n$-dimensional spheres $S^n$ and hemispheres $S^n_+$ when endowed with their chordal metrics. In particular, we show that every compact extended Ptolemy metric space with the property that every three points are contained in a circle is Möbius equivalent to $(S^n,d_0)$ for some $n\ge 1$, the $n$-dimensional sphere $S^n$ with its chordal metric.

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Thomas Foertsch, Viktor Schroeder. 2010-08-19. A Möbius Characterization of Metric Spheres. https://arxiv.org/abs/1008.3250

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