{"paper":{"title":"Configuration Spaces over Singular Spaces -- II. Curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.PR"],"primary_cat":"math.MG","authors_text":"Kohei Suzuki, Lorenzo Dello Schiavo","submitted_at":"2022-05-03T09:07:09Z","abstract_excerpt":"This is the second paper of a series on configuration spaces $\\Upsilon$ over singular spaces $X$. Here, we focus on geometric aspects of the extended metric measure space $(\\Upsilon, \\mathsf{d}_{\\Upsilon}, \\mu)$ equipped with the $L^2$-transportation distance $\\mathsf{d}_{\\Upsilon}$, and a mixed Poisson measure $\\mu$. Firstly, we establish the essential self-adjointness and the $L^p$-uniqueness for the Laplacian on $\\Upsilon$ lifted from $X$. Secondly, we prove the equivalence of Bakry-\\'Emery curvature bounds on $X$ and on $\\Upsilon$, without any metric assumption on $X$. We further prove the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.01379","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/2205.01379/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"}