Volume growth and positive scalar curvature

TL;DR

This paper investigates the volume growth and rigidity properties of three-dimensional non-compact Riemannian manifolds with non-negative Ricci curvature and positive scalar curvature, establishing sharp bounds and characterizations.

Contribution

It provides the first sharp linear volume growth ratio and rigidity results for such manifolds, advancing understanding of their geometric structure.

Findings

Established sharp linear volume growth ratio.

Proved rigidity results for manifolds with specified curvature conditions.

Characterized the geometric structure of the manifolds under study.

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.