Ricci flow and Ricci Limit Spaces

TL;DR

This survey reviews recent advances in Ricci flow theory, especially for flows with unbounded curvature, and discusses their applications to Ricci limit spaces, emphasizing intuitive understanding.

Contribution

It provides a comprehensive overview of developments in Ricci flow with unbounded curvature and its applications to Ricci limit spaces, highlighting recent progress.

Findings

Enhanced understanding of Ricci flows with unbounded curvature

Applications to the structure of Ricci limit spaces

Intuitive explanations of complex concepts

Abstract

I survey some of the developments in the theory of Ricci flow and its applications from the past decade. I focus mainly on the understanding of Ricci flows that are permitted to have unbounded curvature in the sense that the curvature can blow up as we wander off to spatial infinity and/or as we decrease time to some singular time. Applications to the study of Ricci limit spaces are surveyed. I emphasise the intuition behind the subject.