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

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.

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Published 5 July 2013