Regularity and singularity of Ricci curvature and related applications

Wenshuai Jiang (Sydney)

Abstract

In this talk, we will consider Gromov-Hausdorff limit of noncollapsed n-manifolds with lower Ricci curvature bound. It was proved by Cheeger-Colding that the limit space has a regular-singular decomposition such that the singular set has Hausdorff codimension at least 2. In a joint work with Professor Jeff Cheeger and Professor Aaron Naber, we can show that the singular set is (n-2)-rectifiable, and we obtain quantitative estimate of the singular set. As related applications, we will discuss the Bergman kernel estimate of Fano manifold and Nodal set of harmonic functions.