  Riemannian Penrose Inequalities are precise geometric statements that imply
that the total mass of a zero second fundamental form slice of a spacetime is
at least the mass contributed by the black holes, assuming that the spacetime
has nonnegative matter density everywhere. In this paper, we remove this last
assumption, and prove stronger statements that the total mass is at least the
mass contributed by the black holes, plus a contribution coming from the matter
density along the slice.
  We use the first author's conformal flow to achieve this, combined with
Stern's harmonic level set techniques in the first case, and spinors in the
second case. We then compare these new results to results previously known from
Huisken-Ilmanen's inverse mean curvature flow techniques.
