Integral of scalar curvature on non-parabolic manifolds

Abstract

Using the monotonicity formulas of Colding and Minicozzi, we prove that on any complete, non-parabolic Riemannian manifold $(M^3,g)$ with non-negative Ricci curvature, the asymptotic weighted scaling invariant integral of scalar curvature has an explicit bound in form of asymptotic volume ratio.

arXiv commentto appear in J. Geom. Anal