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.