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

TL;DR

This paper extends the positivity proof of a quasi-local mass in general dimensions, originally established by Wang and Yau, under weaker boundary conditions, using methods similar to Eichmair, Miao, and Wang.

Contribution

It demonstrates the positivity of Wang and Yau's quasi-local mass under less restrictive boundary assumptions in higher dimensions.

Findings

Positivity of the quasi-local mass holds under weaker boundary conditions.

The proof adapts methods from Eichmair, Miao, and Wang.

Results apply to general dimensions.

Abstract

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].