Structure theory of singular spaces

摘要

In this paper we develop a structure theory of Einstein manifolds or manifolds with lower Ricci curvature bounds for certain singular spaces that arise as geometric limits of sequences of Riemannian manifolds. This theory generalizes the results that were obtained by Cheeger, Golding and Naber in the smooth setting. In the course of the paper, we will carefully characterize the assumptions that we have to impose on this sequence of Riemannian manifolds in order to guarantee that the individual results hold.