On the conditions to extend Ricci flow(III)

TL;DR

This paper refines curvature estimates and develops volume estimates for Ricci flow with bounded scalar curvature, aiding the analysis of singularities and convergence in Ricci and Kähler Ricci flows.

Contribution

It simplifies and improves previous curvature estimates and introduces volume estimates applicable to Ricci flow singularity analysis and convergence studies.

Findings

Enhanced curvature estimates for Ricci flow

Volume estimates for flows with bounded scalar curvature

Applications to singularity and convergence analysis

Abstract

We simplify and improve the curvature estimates in the paper: On the conditions to extend Ricci flow(II). Furthermore, we develop some volume estimates for the Ricci flow with bounded scalar curvature. These estimates can be applied to study the singularities of the Ricci flow and convergence properties of the K\"ahler Ricci flow.