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arXiv · 2204.09612

Comparison theorems for Lorentzian length spaces with lower timelike curvature bounds

Waldemar Barrera·Luis Montes de Oca·Didier A. Solis
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Abstract

In this article we introduce a notion of normalized angle for Lorentzian pre-length spaces. This concept allows us to prove some equivalences to the definition of timelike curvature bounds from below for Lorentzian pre-length spaces. Specifically, we establish some comparison theorems known as the local Lorentzian version of the Toponogov theorem and the Alexandrov convexity property. Finally, as an application we obtain a first variation Formula for non-negatively curved globally hyperbolic Lorentzian length spaces.

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Waldemar Barrera, Luis Montes de Oca, Didier A. Solis. 2022-04-20. Comparison theorems for Lorentzian length spaces with lower timelike curvature bounds. https://doi.org/10.1007/s10714-022-02989-2

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