Speaker
Christian Ketterer
(Maynooth)
Description
In this talk I will introduce a notion of convergence for Lorentzian prelength spaces called $\ell$-convergence. I present a theorem showing that timelike curvature and curvature-dimension bounds are preserved under $\ell$-convergence of Lorentzian geodesic spaces. Then, I use $\ell$-convergence to study generalized cones, and I show timelike curvature and curvature-dimension bounds. The assumptions are sharp and don't require smoothness. Finally, there is an $\ell$-pre-compactness theorem for the class of smooth generalized cones with a uniform lower bound on the full Ricci tensor.