Geometry Seminar: M. Sánchez Caja (Universidad de Granada)

Geometry Seminar (Geometric Analysis)

Speaker: Miguel Sánchez Caja (Universidad de Granada)

Title: Lorentzian Cheeger-Gromov convergence

Abstract: The difficulties of Cheeger-Gromov convergence in the semi-Riemannian setting will be discussed. First, an anchored convergence (slightly more restrictive than usual Riemannian pointed one) is shown to give satisfactory results for uniqueness of limits under $C^2$ convergence. In the Lorentzian signature, this regularity is lowered and Riemannian results on the existence of limits are made available, by using Cauchy temporal functions as (strongly restrictive) anchors. Links with previous breakthroughs as Sormani-Vega null distance and the role in this setting of h-steep functions by Burstcher and García-Heveling will be stressed. Talk based on joint work with S. Burgos and J.L. Flores, arxiv: 2508.15441.