Title: Lower Bounds on Ricci Curvature and Quantitative Behavior of Singular Sets

Speaker: Feng Wang (Peking University)

Time: Apr 7, 2011, 2:00-4:00 pm

Venue: Room 1328 at BICMR, Resource Plaza, Peking University

Abstract: Let Yn denote the Gromov-Hausdorff limit of a sequence of v-noncollapsed riemannian manifolds with Ric≥ - (n - 1). The singular set S of Y has a stratificationS0 ⊂ S1 ⊂ • • • ⊂ S(n-1), where y ∈ Sk if no tangent cone at y splits off a factor R^(k+1) isometrically. There is a known Hausdorff dimension bound dim Sk ≤ k. Here, we define for all η > 0, 0 < r ≤ 1, the k-th effective singular stratum Sk(η,r) .Sharpening the bound dim Sk ≤ k, we prove that the r-tubular neighborhood satisfies: Vol(Tr(Sk(η,r) ∩ B1(y)) ≤c(n, v, η)rn - k - η, for all y.