Alexandrov's Patchwork and the Bonnet-Myers Theorem for Lorentzian Length Spaces

Explore cutting-edge research in Lorentzian geometry through this 31-minute conference talk delivered at the Workshop on "Non-regular Spacetime Geometry" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into two significant results in the study of global timelike curvature bounds within the Lorentzian length space framework. Discover the construction of a Lorentzian analogue to Alexandrov's Patchwork from metric geometry, demonstrating how suitably nice Lorentzian length spaces with local upper timelike curvature bounds also satisfy corresponding global upper bounds. Examine a Bonnet-Myers style result for spaces with global and negative lower timelike curvature bounds, which constrains their diameter with respect to the time separation function. Gain insights into this collaborative research conducted with Tobias Beran and Lewis Napper, advancing our understanding of non-regular spacetime geometry.