Local pinching estimates in 3-dim Ricci flow

TL;DR

This paper investigates curvature pinching estimates in 3-dimensional Ricci flow without assuming bounded curvature, deriving general conditions preserved under the flow and establishing a local Hamilton-Ivey estimate.

Contribution

It introduces new curvature conditions preserved during Ricci flow on complete 3-manifolds and extends Hamilton-Ivey estimates locally.

Findings

Derived general curvature conditions preserved under Ricci flow

Established local Hamilton-Ivey estimates

Included nonnegative Ricci and sectional curvature as special cases

Abstract

We study curvature pinching estimates of Ricci flow on complete 3- dimensional manifolds without bounded curvature assumption. We will derive some general curvature conditions which are preserved on any complete solution of 3-dim Ricci flow, these conditions include nonnegative Ricci curvature and sectional curvature as special cases. A local version of Hamilton-Ivey estimates is also obtained.