Implications of some mass-capacity inequalities

TL;DR

This paper explores mass-capacity inequalities to establish conditions ensuring nonnegative and positively bounded mass on certain manifolds with nonnegative scalar curvature, including cases with singularities.

Contribution

It introduces new sufficient conditions based on mass-capacity inequalities that guarantee nonnegative and positive mass bounds on manifolds with scalar curvature constraints.

Findings

Mass is nonnegative under certain conditions.

Positive lower bounds for mass are established.

Results apply to manifolds with or without singularities.

Abstract

Applying a family of mass-capacity related inequalities proved in \cite{M22}, we obtain sufficient conditions that imply the nonnegativity as well as positive lower bounds of the mass, on a class of manifolds with nonnegative scalar curvature, with or without a singularity.