{"paper":{"title":"Causal convergence conditions through variable timelike Ricci curvature bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MG","math.MP"],"primary_cat":"math-ph","authors_text":"Mathias Braun, Robert J. McCann","submitted_at":"2023-12-28T17:47:12Z","abstract_excerpt":"We describe a nonsmooth notion of globally hyperbolic, regular length metric spacetimes $(\\mathrm{M},l)$. It is based on ideas of Kunzinger-S\\\"amann, but does not require Lipschitz continuity of causal curves. We study geodesics on $\\mathrm{M}$ and the space of probability measures over $\\mathrm{M}$ in detail.\n  Furthermore, for such a spacetime endowed with a reference measure $\\mathfrak{m}$, a lower semicontinuous function $k\\colon \\mathrm{M} \\to \\textbf{R}$, and constants $0<p<1$ and $N\\geq 1$, we introduce and study the entropic timelike curvature dimension condition $\\smash{\\mathrm{TCD}_p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.17158","kind":"arxiv","version":2},"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/2312.17158/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"}