# Regularity theory for Type I Ricci flows

## TL;DR

This paper develops integral curvature estimates for Type I Ricci flows up to singularities, extending previous results to higher dimensions using adapted quantitative stratification techniques.

## Contribution

It introduces a new application of quantitative stratification to higher-dimensional Ricci flows, providing integral curvature bounds near singularities.

## Key findings

- Integral estimates for curvature tensor up to singular time
- Extension of 3D curvature estimates to higher dimensions
- Application of quantitative stratification in Ricci flow analysis

## Abstract

We consider Type I Ricci flows and obtain integral estimates for the curvature tensor valid up to, and including, the singular time. Our estimates partially extend to higher dimensions a curvature estimate recently shown to hold in dimension three by Kleiner and Lott. To do this we adapt the technique of quantitative stratification, introduced by Cheeger and Naber, to this setting.