Space of Ricci Flows I

Abstract

Abstract In this paper, we study the moduli spaces of m ‐dimensional, κ‐noncollapsed Ricci flow solutions with bounded $\int |Rm|^{{m}/{2}}$ and bounded scalar curvature. We show a weak compactness theorem for such moduli spaces and apply it to study the estimates of isoperimetric constants, the Kähler‐Ricci flows, and the moduli spaces of gradient shrinking solitons. © 2012 Wiley Periodicals, Inc.