  The Positive Mass Theorem states that a complete asymptotically flat manifold
of nonnegative scalar curvature has nonnegative mass. The Riemannian Penrose
inequality provides a sharp lower bound for the mass when black holes are
present. More precisely, this lower bound is given in terms of the area of an
outermost minimal surface, and equality is achieved only for Schwarzschild
metrics. The Riemannian Penrose inequality was first proved in three dimensions
in 1997 by G. Huisken and T. Ilmanen for the case of a single black hole. In
1999, H. Bray extended this result to the general case of multiple black holes
using a different technique. In this paper we extend Bray's technique to
dimensions less than 8.
