Three-manifolds with bounded curvature and uniformly positive scalar curvature

TL;DR

This paper proves that three-dimensional noncompact Riemannian manifolds with bounded sectional curvature and uniformly positive scalar curvature have a uniform lower bound on their injectivity radius.

Contribution

It establishes a new link between scalar curvature positivity and injectivity radius bounds in three-manifolds with bounded sectional curvature.

Findings

Uniform lower bound on injectivity radius established

Conditions relate scalar curvature positivity to geometric bounds

Results apply to complete noncompact three-manifolds

Abstract

In this note, we prove that for a complete noncompact three dimensional Riemannian manifold with bounded sectional curvature, if it has uniformly positive scalar curvature, then there is a uniform lower bound on the injectivity radius.