{"paper":{"title":"Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jeffrey S. Case","submitted_at":"2007-12-09T20:40:58Z","abstract_excerpt":"We consider the Hawking-Penrose singularity theorems and the Lorentzian splitting theorem under the weaker curvature condition of nonnegative Bakry-Emery-Ricci curvature $Ric_f^m$ in timelike directions. We prove that they still hold when $m$ is finite, and when $m$ is infinite, they hold under the additional assumption that $f$ is bounded from above."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1321","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":""},"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"}