{"paper":{"title":"Lower Ricci Curvature, Branching, and Bi-Lipschitz Structure of Uniform Reifenberg Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Aaron Naber, Tobias Holck Colding","submitted_at":"2011-11-09T12:09:19Z","abstract_excerpt":"We study here limit spaces $(M_\\alpha,g_\\alpha,p_\\alpha)\\stackrel{GH}{\\rightarrow} (Y,d_Y,p)$, where the $M_\\alpha$ have a lower Ricci curvature bound and are volume noncollapsed. Such limits $Y$ may be quite singular, however it is known that there is a subset of full measure $\\cR(Y)\\subseteq Y$, called {\\it regular} points, along with coverings by the almost regular points $\\cap_\\epsilon \\cup_r\\cR_{\\epsilon,r}(Y)=\\cR(Y)$ such that each of the {\\it Reifenberg sets} $\\cR_{\\epsilon,r}(Y)$ is bi-H\\\"older homeomorphic to a manifold. It has been an ongoing question as to the bi-Lipschitz regularit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2184","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":""},"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"}