# Relative volume comparison of Ricci Flow and its applications

## TL;DR

This paper develops a new volume comparison estimate for Ricci flow, extending Perelman's no local collapsing estimate, and applies it to analyze the convergence of Kähler-Ricci flow on minimal manifolds.

## Contribution

It introduces a generalized volume comparison estimate for Ricci flow, analogous to Bishop-Gromov, and demonstrates its application to Kähler-Ricci flow convergence.

## Key findings

- Derived a relative volume comparison estimate for Ricci flow
- Extended Perelman's no local collapsing estimate
- Applied the estimate to Gromov-Hausdorff convergence of Kähler-Ricci flow

## Abstract

In this paper, we derive a relative volume comparison estimate along Ricci flow and apply it to studying the Gromov-Hausdorff convergence of K\"ahler-Ricci flow on a minimal manifold. This new estimate generalizes Perelman's no local collapsing estimate and can be regarded as an analogue of the Bishop-Gromov volume comparison for Ricci flow.