Injectivity radius bound of Ricci flow with positive Ricci curvature and applications

TL;DR

This paper establishes bounds on the injectivity radius for 3-dimensional Ricci flow with positive Ricci curvature and demonstrates long-term existence, addressing a question from a well-known geometry text.

Contribution

It provides new injectivity radius bounds for Ricci flow under positive Ricci curvature and applies these results to prove long-time existence, partially answering an open question.

Findings

Injectivity radius bounds for 3D Ricci flow with positive Ricci curvature

Long-time existence of Ricci flow under these conditions

Partial resolution of a question from Chow-Lu-Ni (2006)

Abstract

In this paper, we study the injectivity radius bound for 3-d Ricci flow. As applications we show the long time existence of the Ricci flow with positive Ricci curvature. We also partially settle a question in page 302 of the book of Chow-Lu-Ni (2006).