{"paper":{"title":"Warped products over one-dimensional base spaces and the RCD condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Christian Ketterer","submitted_at":"2025-06-12T15:24:18Z","abstract_excerpt":"We prove the Riemannian curvature-dimension condition $\\mathsf{RCD}(KN,N+1)$ for an $N$-warped product $B\\times_f^N F$ over a one-dimensional base space $B$ with a Lipschitz function $f: B\\rightarrow \\mathbb R_{\\geq 0}$, provided (1) $f$ is a $Kf$-concave function, (2) $f$ satisfies a sub-Neumann boundary condition $\\frac{\\partial f}{\\partial n}\\geq 0$ on $\\partial B\\backslash f^{-1}(0)$ and $F$ is a compact metric measure space satisfying (3) the condition $\\mathsf{RCD}(K_F (N-1), N)$ with $K_F:= \\sup_B \\{ (Df)^2 + Kf^2\\}$. The result is sharp, i.e. we show that (1), (2) and (3) are necessary"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.10809","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/2506.10809/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"}