Collapsing shells and the isoperimetric inequality for black holes

Recent results of Trudinger on isoperimetric inequalities for non-convex bodies are applied to the gravitational collapse of a lightlike shell of matter to form a black hole. Using some integral identities for co-dimension-two surfaces in Minkowski spacetime, the area A of the apparent horizon is shown to be bounded above in terms of the mass M by , which is consistent with the cosmic censorship hypothesis. The results hold in four spacetime dimensions and above.