Equivalence between the timelike Brunn-Minkowski inequality and timelike Bakry-Émery-Ricci lower bound on weighted globally hyperbolic spacetimes

Osama Farooqui

We prove the timelike Brunn-Minkowski inequality $\mathsf{TBM}(K,N)$ implies a timelike lower bound on the Bakry-Émery-Ricci curvature on weighted globally hyperbolic spacetimes. T…