quasi-local mass quantity is defined in [16] for fill-ins (Ω,g)∈ ̊F(Σ,γ)as follows:m(Ω,g) := Λ(Σ,γ)−18π∫ΣHgdσ.(1.7)HereHgis the mean curvature of the boundary Σ with respect to theunit outward norma