Geometry & Topology

Event Information Quantitative Estimates on the Singular Sets of Alexandrov Spaces
16:10 on Monday December 04, 2017
17:00 on Monday December 04, 2017
BA6183, Bahen Center, 40 St. George St.
Nan Li

CUNY

The notion of quantitative singular sets for spaces with lower Ricci curvature bounds was initiated by Cheeger and Naber. Volume estimates were proved for these singular sets in a non-collapsing setting. For Alexandrov spaces, we obtain stronger and volume-free estimates. We also show that the $(k,\epsilon)$-singular sets are $k$-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber.