Scalar curvature lower bound under integral convergence

Yiqi Huang, Man-Chun Lee

Published 2021-11-09, updated 2022-09-27Version 2

In this work, we consider sequences of $C^2$ metrics which converge to a $C^2$ metric in $C^0$ sense. We show that if the scalar curvature of the sequence is almost non-negative in the integral sense, then the limiting metric has scalar curvature lower bound in point-wise sense.