Communications in Analysis and Geometry

Volume 21 (2013)

Number 4

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

Pages: 847 – 871



Kwok-Kun Kwong (School of Mathematical Sciences, Monash University, Victoria, Australia)


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.

Published 5 July 2013