Space of Ricci flows (I)

TL;DR

This paper investigates the structure and properties of moduli spaces of noncollapsed Ricci flow solutions, establishing compactness results and applications to isoperimetric constants, Kähler Ricci flow, and gradient shrinking solitons.

Contribution

It introduces a weak compactness theorem for moduli spaces of Ricci flows with bounded energy and scalar curvature, advancing understanding of their geometric properties.

Findings

Established a weak compactness theorem for Ricci flow moduli spaces

Applied results to control isoperimetric constants in Ricci flows

Analyzed implications for Kähler Ricci flow and gradient shrinking solitons

Abstract

In this paper, we study the moduli spaces of noncollapsed Ricci flow solutions with bounded energy and scalar curvature. We show a weak compactness theorem for such moduli spaces and apply it to study isoperimetric constant control, K\"ahler Ricci flow and moduli space of gradient shrinking solitons.