  We prove the following stronger verson of the positivity of quasi-local mass
stated in gr-qc/0303019: the quasi-local energy (mass) of each connected
component of the boundary of a compact spacelike hypersurface which satisfies
the local energy condition is strictly positive unless the spacetime is flat
along the spacelike hypersurface and the boundary of the spacelike hypersurface
is connected.
