{"paper":{"title":"A Remark on Regular Points of Ricci Limit Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Lina Chen","submitted_at":"2015-08-28T06:22:06Z","abstract_excerpt":"Let $Y$ be a Gromov-Hausdorff limit of complete Riemannian n-manifolds with Ricci curvature bounded from below.\n  A point in $Y$ is called $k$-regular, if its tangent is unique and is isometric to an $k$-dimensional Euclidean space.\n  By \\cite{B5}, there is $k>0$ such that the set of all $k$-regular point $\\mathcal{R}_k$ has a full renormalized measure.\n  An open problem is if $\\mathcal{R}_l=\\emptyset$ for all $l<k$? The main result in this paper asserts that if $\\mathcal{R}_1\\ne \\emptyset$, then $Y$ is a one dimensional topological manifold. Our result improves the Handa's result \\cite{Honda}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07105","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":""},"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"}