Implications of some mass-capacity inequalities

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.

arXiv commentimproved exposition, 14 pages, 1 figure, to appear in the Journal of Geometric Analysis

References in corpus (6)

• Scalar curvature and singular metrics
• On The Capacity of Surfaces in Manifolds with Nonnegative Scalar Curvature
• Positive scalar curvature with skeleton singularities
• Mass, capacitary functions, and the mass-to-capacity ratio
• Zero area singularities in general relativity and inverse mean curvature flow
• Some rigidity results for the Hawking mass and a lower bound for the Bartnik capacity