Geometric Analysis Seminar ——The structure of the singular set of Ricci limit spaces
报告人：Wenshuai Jiang（Zhejiang University）
时间：2018-10-10 08:00-10:00
地点：Room 1114, Sciences Building No. 1
Abstract: In this talk, we will consider the Gromov-Hausdorff limit space (X,d) of a sequence of n-manifolds
with lower Ricci curvature bound and noncollapsed volume. The limit space has a singular-regular
decomposition X=R\cup S and dim S<=n-2 proved by Cheeger-Colding. In this talk we will study the structure
of the singular set S and show that the singular set is (n-2)-rectifiable. We will also discuss the quantitative
estimate of the singular set. The proofs are based on some new estimates on neck regions and a
decomposition the orem which covers a general ball by neck regions and good balls. Our main focus in this talk
is the proof of the decomposition theorem. This is a joint work with Jeff Cheeger and Aaron Naber.
