{"paper":{"title":"Non-collapsed eGH convergence and dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Jaime Santos-Rodr\\'iguez, Jes\\'us N\\'u\\~nez-Zimbr\\'on, Sergio Zamora","submitted_at":"2025-09-26T18:29:22Z","abstract_excerpt":"Let $(X_i,p_i)$ be a non-collapsing sequence of pointed $n$-dimensional Riemannian manifolds with a uniform lower Ricci curvature bound, and $ G_i \\leq \\operatorname{Iso} (X_i)$ a sequence of closed subgroups of isometries. We show that if the triples $(X_i, G_i, p_i)$ converge in the equivariant Gromov--Hausdorff sense to a triple $(X,G,p)$, then $\\operatorname{dim} (G) \\geq \\limsup _{i \\to \\infty} \\operatorname{dim} (G_i)$, generalizing a result of Mazur--Rong--Wang to the non-compact setting.\n  The argument also applies in the non-smooth setting of $\\operatorname{RCD}$ spaces. As an applica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.22821","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/2509.22821/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"}