# Another proof of the local curvature estimate for the Ricci flow

## TL;DR

This paper presents a new, simplified proof of a recent result on local curvature estimates in Ricci flow, utilizing the De Giorgi iteration method to establish bounds based on initial conditions and Ricci curvature constraints.

## Contribution

It introduces a novel, streamlined proof technique for existing local curvature estimates in Ricci flow using De Giorgi iteration.

## Key findings

- Established local boundedness of Riemannian curvature tensor
- Provided a simpler proof of existing curvature estimates
- Linked curvature bounds to initial data and Ricci curvature bounds

## Abstract

By using the De Giorgi iteration method we will give a new simple proof of the recent result of B.Kotschwar, O.Munteanu, J.Wang [KMW] and N.Sesum [S] on the local boundedness of the Riemmanian curvature tensor of solutions of Ricci flow in terms of its inital value on a given ball and a local uniform bound on the Ricci curvature.