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

We present key initial results in the study of global timelike curvature bounds within the Lorentzian pre-length space framework. Most notably, 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.Comment: 34 pages, 6 figure