Equivalence between the timelike Brunn-Minkowski inequality and timelike Bakry-Émery-Ricci lower bound on weighted globally hyperbolic spacetimes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913783555817472 |
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| author | Farooqui, Osama |
| author_facet | Farooqui, Osama |
| contents | 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. This result, together with the well-known equivalence between timelike Bakry-Émery-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06186 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivalence between the timelike Brunn-Minkowski inequality and timelike Bakry-Émery-Ricci lower bound on weighted globally hyperbolic spacetimes Farooqui, Osama Metric Geometry General Relativity and Quantum Cosmology 49Q22 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. This result, together with the well-known equivalence between timelike Bakry-Émery-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. |
| title | Equivalence between the timelike Brunn-Minkowski inequality and timelike Bakry-Émery-Ricci lower bound on weighted globally hyperbolic spacetimes |
| topic | Metric Geometry General Relativity and Quantum Cosmology 49Q22 |
| url | https://arxiv.org/abs/2504.06186 |