{"paper":{"title":"Equivalence between the timelike Brunn-Minkowski inequality and timelike Bakry-\\'Emery-Ricci lower bound on weighted globally hyperbolic spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.MG","authors_text":"Osama Farooqui","submitted_at":"2025-04-08T16:28:07Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.06186","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.06186/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}