Remark about scalar curvature on certain noncompact manifolds

TL;DR

This paper establishes conditions preventing certain noncompact manifolds from admitting complete metrics with nonnegative scalar curvature and provides examples of manifolds with positive scalar curvature in higher dimensions.

Contribution

It introduces a sufficient condition to exclude nonnegative scalar curvature metrics on handlebody interiors and constructs examples of positive scalar curvature ends in higher dimensions.

Findings

Sufficient condition to rule out nonnegative scalar curvature on handlebody interiors

Examples of manifolds with positive scalar curvature in higher dimensions

Insights into scalar curvature behavior on noncompact manifolds

Abstract

We give a sufficient condition to rule out complete Riemannian metrics with nonnegative scalar curvature on the interiors of handlebodies. In higher dimensions, we give examples of ends of manifolds with positive scalar curvature metrics.