Structure theory of singular spaces

TL;DR

This paper extends the structure theory of Riemannian manifolds to certain singular spaces, providing a foundation for analyzing Ricci flows with bounded curvature.

Contribution

It generalizes existing geometric analysis theories to singular spaces, enabling new applications in Ricci flow analysis.

Findings

Development of a generalized structure theory for singular spaces

Framework for analyzing limits of Riemannian manifolds with singularities

Foundation for future work on Ricci flows with bounded curvature

Abstract

In this paper we generalize the theory of Cheeger, Colding and Naber to certain singular spaces that arise as limits of sequences of Riemannian manifolds. This theory will have applications in the analysis of Ricci flows of bounded curvature, which we will describe in a subsequent paper.