On the $L^{n\over 2}$-norm of Scalar Curvature

TL;DR

This paper investigates the relationships between the $L^{n/2}$-norms of scalar curvatures of Riemannian metrics and standard metrics, focusing on conformal classes and specific curvature conditions.

Contribution

It provides new comparison results for $L^{n/2}$-norms of scalar curvature within conformal classes and under particular curvature constraints.

Findings

Established bounds for $L^{n/2}$-norms of scalar curvature

Identified conditions under which the norms compare favorably

Extended previous results to broader classes of metrics

Abstract

Comparisons on $L^{n\over 2}$-norms of scalar curvatures between Riemannian metrics and standard metrics are obtained. The metrics are restricted to conformal classes or under certain curvature conditions.