{"paper":{"title":"Characterization of Tangent Cones of Noncollapsed Limits with Lower Ricci Bounds and Applications","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":"2011-08-16T14:15:27Z","abstract_excerpt":"Consider a limit space $(M_\\alpha,g_\\alpha,p_\\alpha)\\stackrel{GH}{\\rightarrow} (Y,d_Y,p)$, where the $M_\\alpha^n$ have a lower Ricci curvature bound and are volume noncollapsed. The tangent cones of $Y$ at a point $p\\in Y$ are known to be metric cones $C(X)$, however they need not be unique. Let $\\bar\\Omega_{Y,p}\\subseteq\\cM_{GH}$ be the closed subset of compact metric spaces $X$ which arise as cross sections for the tangents cones of $Y$ at $p$. In this paper we study the properties of $\\bar\\Omega_{Y,p}$. In particular, we give necessary and sufficient conditions for an open smooth family $\\O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3244","kind":"arxiv","version":3},"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"}