Andrea Mondino (University of Oxford)
Title: A sharp isoperimetric-type inequality for Lorentzian spaces satisfying time-like Ricci lower bounds
Abstract:
In the seminar, I will present recent joint work with Fabio Cavalletti (Milan),
establishing a sharp and rigid isoperimetric-type inequality in Lorentzian
signature under the assumption of Ricci curvature bounded below in the time-like
directions. The inequality is proved in the high generality of Lorentzian length
spaces satisfying time-like Ricci curvature lower bounds in a synthetic sense
via optimal transport. The results are new already for smooth Lorentzian
manifolds. Applications include an upper area bound of Cauchy hypersurfaces
inside the interior of a black hole and an upper bound on the area of Cauchy
hypersurfaces in cosmological space-times.