A note on the positivity of a quasi-local mass in general dimensions

Wang and Yau [10] introduced a quasi-local mass, which is a hyperbolic background generalization of Liu-Yau's expression [7] [8], and proved its positivity. In this note, we prove that the positivity of this quasi-local mass is still valid under weaker assumptions on the boundary hypersurface in general dimensions. The method we used is similar to that used by Eichmair, Miao and Wang in [4].