Global $\varepsilon$-regularity for 4-dimensional Ricci flow with integral scalar curvature bound

TL;DR

This paper extends the global epsilon-regularity results for 4-dimensional Ricci flow from bounded scalar curvature to cases with an integral scalar curvature bound, broadening the applicability of regularity criteria.

Contribution

It introduces a new epsilon-regularity theorem for 4D Ricci flow under integral scalar curvature bounds, generalizing previous bounded scalar curvature results.

Findings

Established epsilon-regularity under integral scalar curvature bounds

Extended regularity criteria to broader curvature conditions

Provided new tools for analyzing 4D Ricci flow behavior

Abstract

Ge-Jiang (Geom Funct Anal 27:1231-1256, 2017) proved global $\varepsilon$-regularity for 4-dimensional Ricci flow with bounded scalar curvature. In this note, we extend this result to 4-dimensional Ricci flow with integral bound on the scalar curvature.