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arXiv · 2601.21596

Lorentz meets Ptolemy

Felix Rott·Zhe-Feng Xu·Matteo Zanardini
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Abstract

We consider a Lorentzian analogue of the Ptolemy inequality and we prove that in the setting of globally hyperbolic spacetimes it is equivalent to a global timelike sectional curvature bound from above by zero. We investigate the link between the Ptolemy inequality and the hyperbolic inversion and establish some applications and rigidity properties.

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Felix Rott, Zhe-Feng Xu, Matteo Zanardini. 2026-01-29. Lorentz meets Ptolemy. https://arxiv.org/abs/2601.21596

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