COLLAPSING SHELLS AND THE ISOPERIMETRIC INEQUALITY FOR BLACK-HOLES

Recent results of Trudinger on isoperimetric inequalities for non-conv ex bodies are applied to the gravitational collapse of a lightlike she ll of matter to form a black hole. Using some integral identities for co-dimension-two surfaces in Minkowski spacetime, the area A of the ap parent horizon is shown to be bounded above in terms of the mass M by 16 pi G(2)M(2), which is consistent with the cosmic censorship hypothe sis. The results hold in four spacetime dimensions and above.