Volume growth and positive scalar curvature

Abstract

For three dimensional complete, non-compact Riemannian manifolds with non-negative Ricci curvature and uniformly positive scalar curvature, we obtain the sharp linear volume growth ratio and the corresponding rigidity.

arXiv commentsubmitted to some journal

References in corpus (7)

• Generalized soap bubbles and the topology of manifolds with positive scalar curvature
• Geometry of positive scalar curvature on complete manifold
• Geometry of three-dimensional manifolds with positive scalar curvature
• Integral of scalar curvature on manifolds with a pole
• Complete stable minimal hypersurfaces in positively curved 4-manifolds
• Sweeping out 3-manifold of positive Ricci curvature by short 1-cycles via estimates of min-max surfaces
• Volume growth of 3-manifolds with scalar curvature lower bounds