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arXiv · 2504.06186

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

Osama Farooqui
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Abstract

We prove the timelike Brunn-Minkowski inequality $\mathsf{TBM}(K,N)$ implies a timelike lower bound on the Bakry-\'Emery-Ricci curvature on weighted globally hyperbolic spacetimes. This result, together with the well-known equivalence between timelike Bakry-\'Emery-Ricci lower bounds and the $\mathsf{TCD}(K,N)$ condition, and the fact that $\mathsf{TCD}(K,N)$ spaces support the timelike Brunn-Minkowski inequality, draws an equivalence between $\mathsf{TBM}(K,N)$ and $\mathsf{TCD}(K,N)$ in the smooth setting.

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Osama Farooqui. 2025-04-08. Equivalence between the timelike Brunn-Minkowski inequality and timelike Bakry-\'Emery-Ricci lower bound on weighted globally hyperbolic spacetimes. https://arxiv.org/abs/2504.06186

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