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arXiv · 2302.11615

Alexandrov's Patchwork and the Bonnet--Myers Theorem for Lorentzian length spaces

Tobias Beran·Lewis Napper·Felix Rott
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Abstract

We present several key results for Lorentzian pre-length spaces with global timelike curvature bounds. Most significantly, we construct a Lorentzian analogue to Alexandrov's Patchwork, thus proving that suitably nice Lorentzian pre-length spaces with local upper timelike curvature bound also satisfy a corresponding global upper bound. Additionally, for spaces with global lower bound on their timelike curvature, we provide a Bonnet--Myers style result, constraining their finite diameter. Throughout, we make the natural comparisons to the metric case, concluding with a discussion of potential applications and ongoing work.

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Tobias Beran, Lewis Napper, Felix Rott. 2023-02-22. Alexandrov's Patchwork and the Bonnet--Myers Theorem for Lorentzian length spaces. https://arxiv.org/abs/2302.11615

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