Global Regularity of Three-Dimensional Ricci Limit Spaces

TL;DR

This paper proves that all three-dimensional Ricci limit spaces are globally homeomorphic to smooth manifolds with local bi-Holder regularity, extending previous work through the construction of specialized Ricci flows.

Contribution

It introduces a method to establish global homeomorphisms from 3D Ricci limit spaces to smooth manifolds, utilizing local pyramid Ricci flows inspired by Hochard.

Findings

Established a global homeomorphism for 3D Ricci limit spaces.

Constructed local pyramid Ricci flows on uniform regions.

Extended previous results by Simon and the second author.

Abstract

We construct a global homeomorphism from any 3D Ricci limit space to a smooth manifold, that is locally bi-Holder. This extends the recent work of Miles Simon and the second author, and we build upon their techniques. A key step in our proof is the construction of local "pyramid Ricci flows", existing on uniform regions of spacetime, that are inspired by Hochard's partial Ricci flows.