Constructing Distance Realizers via Midpoints in Lorentzian Mid-Length Space

Explore a 42-minute conference talk from the Workshop on "Non-regular Spacetime Geometry" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into the world of Lorentzian pre-length spaces with an anti-Lipschitz time function, focusing on the null distance for which the space is complete. Discover how ε-midpoints or midpoints between timelike related points, when appropriately bounded away, can be used to construct a (nearly) distance realizer. Learn about this joint work by Tobias Beran and Felix Rott, which contributes to the understanding of non-regular spacetime geometry and its mathematical foundations.