On the definition of averagely trapped surfaces

Abstract. Previously suggested definitions of averagely trapped surfaces are not welldefined 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 16πM > A, with similar inequalities existing for other definitions of quasi-local energy.