On the positivity of a quasi-local mass in general dimensions

Abstract

In this paper, we obtain a positivity result of a quasi-local mass integral as proposed by Shi and Tam in general dimensions. The main argument is based on the monotonicity of a mass integral in a foliation of quasi-spherical metrics and a positive mass type theorem which was proved by Wang and Yau in the three dimensional case, and is shown here in higher dimensions using spinor methods.

Typos corrected. Some examples added. To appear in Communications in Analysis and Geometry. Any comments welcome!