A Sharp Isoperimetric-Type Inequality for Lorentzian Spaces Satisfying Time-Like Ricci Curvature Lower Bounds

Explore a cutting-edge seminar on Lorentzian geometry and synthetic curvature bounds presented at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into recent joint research establishing a sharp and rigid isoperimetric-type inequality in Lorentzian signature under time-like Ricci curvature lower bounds. Discover how this groundbreaking work applies to both smooth Lorentzian manifolds and more general Lorentzian length spaces using optimal transport techniques. Examine fascinating applications, including upper area bounds for Cauchy hypersurfaces within black hole interiors and cosmological space-times. Gain insights into the intersection of differential geometry, general relativity, and optimal transport theory in this 49-minute talk from the Workshop on "Synthetic Curvature Bounds for Non-Smooth Spaces: Beyond Finite Dimension."