Lorentz meets Ptolemy

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Felix Rott, Zhefeng Xu, Matteo Zanardini
DOI: 10.48550/arxiv.2601.21596
Cited by: 0

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.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Advanced Differential Geometry Research Relativity and Gravitational Theory

Publication details

Journal / source
arXiv (Cornell University)
Publication date
29 January 2026
Document type
Preprint