Local smoothing results for the Ricci flow in dimensions two and three

TL;DR

This paper develops local estimates for Ricci flow solutions in two and three dimensions without requiring bounded curvature, extending Perelman's pseudolocality results to broader settings.

Contribution

It introduces new local smoothing estimates for Ricci flow in low dimensions without curvature bounds, generalizing key pseudolocality results.

Findings

Extended pseudolocality results in 2D Ricci flow

Local estimates applicable without curvature bounds

Implications for geometric analysis of Ricci flow

Abstract

We present local estimates for solutions to the Ricci flow, without the assumption that the solution has bounded curvature. These estimates lead to a generalisation of one of the pseudolocality results of G.Perelman in dimension two.