On the improved no-local-collapsing theorem of Ricci flow

TL;DR

This paper presents an improved no-local-collapsing theorem for Ricci flow, refining Perelman's original result by incorporating scalar curvature bounds along the basepoint's worldline.

Contribution

It introduces a refined version of Perelman's no-local-collapsing theorem under scalar curvature bounds along the basepoint's worldline.

Findings

Enhanced no-local-collapsing estimate for Ricci flow

Refinement of Perelman's theorem with scalar curvature condition

Potential applications to Ricci flow analysis and singularity formation

Abstract

In this note we derive an improved no-local-collapsing theorem of Ricci flow under the scalar curvature bound condition along the worldline of the basepoint. It is a refinement of Perelman's no-local-collapsing theorem.