{"paper":{"title":"Rectifiability of Singular Sets in Noncollapsed Spaces with Ricci Curvature bounded below","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Aaron Naber, Jeff Cheeger, Wenshuai Jiang","submitted_at":"2018-05-21T11:09:55Z","abstract_excerpt":"This paper is concerned with the structure of Gromov-Hausdorff limit spaces $(M^n_i,g_i,p_i)\\stackrel{d_{GH}}{\\longrightarrow} (X^n,d,p)$ of Riemannian manifolds satisfying a uniform lower Ricci curvature bound $Rc_{M^n_i}\\geq -(n-1)$ as well as the noncollapsing assumption $Vol(B_1(p_i))>v>0$. In such cases, there is a filtration of the singular set, $S_0\\subset S_1\\cdots S_{n-1}:= S$, where $S^k:= \\{x\\in X:\\text{ no tangent cone at $x$ is }(k+1)\\text{-symmetric}\\}$; equivalently no tangent cone splits off a Euclidean factor $\\mathbb{R}^{k+1}$ isometrically. Moreover, by \\cite{ChCoI}, $\\dim S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07988","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"}