Schoen-Yau theorem

This article describes a result related to the Ricci curvature of a Riemannian manifold

Statement

Any three-dimensional open positively Ricci-curved Riemannian manifold is diffeomorphic to $\mathbb {R} ^{3}$.

Relation with other results

Zhu's theorem

Further information: Zhu's theorem

This relaxes the positivity assumption of Ricci curvature to a nonnegativity assumption, but places a further restriction that the manifold involved should be complete.