Stability of Positive Mass Theorem for Static Quasi-Local Energy of Compact (Locally) Hyperbolic Graphical Manifolds

In this paper, we consider compact graphical manifolds with boundary over (locally) hyperbolic static space. We prove the stability of the positive mass theorem with respect to the Federer–Fleming flat distance for the static quasi-local Brown-York energy of the outer boundary of compact (locally) hyperbolic graphical manifolds.