Quantitative Estimates on the Singular Sets of Alexandrov Spaces

Nan Li, Aaron Naber

Let $X\in \text{Alex}{}^n(-1)$ be an $n$-dimensional Alexandrov space with curvature $\ge -1$. Let the $r$-scale $(k,\epsilon )$-singular set ${\mathcal{S}}_{\epsilon ,r}^k(X)$ be the collection of…