EVENT DETAILS AND ABSTRACT

Title: Regularity of manifolds with bounded Ricci curvature and the codimension 4 conjecture
Speaker: Jeff Cheeger
Speaker Info: NYU
Brief Description:
Special Note:
Abstract:

This talk concerns joint work with Aaron Naber. We will indicate a proof of the conjecture that a noncollapsed Gromov-Hausdorff limit space of a sequence of manifolds Mⁿ_i with a uniform bound on Ricci curvature is smooth off a closed subset of Hasudorff (or Minkowski) codimension 4. We combine this result with quantitative stratification theory to prove local a priori L_q estimates on the full curvature tensor, for all q<2. In the case of Einstein manifolds, we improve this to estimates on the regularity scale. We also prove a conjecture of Anderson to the effect that the collection of 4-manifolds with |Ric_M⁴|≤ 3, Vol(M⁴) > v > 0 and diam(M⁴)< D, contains at most a finite number of diffeomorphism types. A local version of this is used to show that noncollapsed 4-manifolds with bounded Ricci curvature satisfy a priori L₂ Riemannian curvature estimates.