Scalar curvature lower bound under integral convergence

Abstract

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.

final version, 11 pages, minor mistakes corrected

References in corpus (3)

• On the Distributional Hessian of the Distance Function
• Pointwise lower scalar curvature bounds for $C^0$ metrics via regularizing Ricci flow
• Weak scalar curvature lower bounds along Ricci flow