Integral of scalar curvature on manifolds with a pole

Abstract

On any complete three dimensional Riemannian manifold with a pole and non-negative Ricci curvature, we show that the asymptotic scaling invariant integral of scalar curvature, is equal to a term determined by the asymptotic volume ratio of this Riemannian manifold.

arXiv commentA formula is proved, to appear in Proceedings of the American Mathematical Society

References in corpus (3)

• Geometry of positive scalar curvature on complete manifold
• Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds
• Inverse mean curvature flow and Ricci-pinched three-manifolds

Cited by in corpus (1)

• Volume growth and positive scalar curvature