Lower Ricci Curvature and Nonexistence of Manifold Structure

Erik Hupp, Aaron Naber, Kai-Hsiang Wang

It is known that a limit $(M_j^n,g_j)\to (X^k,d)$ of manifolds $M_j$ with uniform lower bounds on Ricci curvature must be $k$-rectifiable for some unique $\dim X:= k\leq n = \dim M…