  Previously suggested definitions of averagely trapped surfaces are not
well-defined properties of 2-surfaces, and can include surfaces in flat
space-time. A natural definition of averagely trapped surfaces is that the
product of the null expansions be positive on average. A surface is averagely
trapped in the latter sense if and only if its area $A$ and Hawking mass $M$
satisfy the isoperimetric inequality $16\pi M^2 > A$, with similar inequalities
existing for other definitions of quasi-local energy.
