We present two results in the study of global timelike curvature bounds within the Lorentzian length space framework. On the one hand, we construct a Lorentzian analogue to Alexandrov’s Patchwork from metric geometry, thus proving that suitably nice Lorentzian length spaces with local upper timelike curvature bound also satisfy a corresponding global upper bound. On the other hand, for spaces with global and negative lower timelike curvature bounds, we provide a Bonnet–Myers style result, constraining their diameter (with respect to the time separation function).
Joint work with Tobias Beran and Lewis Napper.