  Consider a one-parameter family of smooth Riemannian metrics on a two-sphere,
$\mathscr{S}$. By choosing a one-parameter family of smooth lapse and shift,
these Riemannian two-spheres can always be assembled into smooth Riemannian
three-space, with metric $h_{ij}$ on a three-manifold $\Sigma$ foliated by a
one-parameter family of two-spheres $\mathscr{S}_\rho$. It is shown first that
we can always choose the shift such that the $\mathscr{S}_\rho$ surfaces form a
smooth inverse mean curvature foliation of $\Sigma$. An integrodifferential
expression, referring only to the area of the level sets and the lapse
function, is also derived that can be used to quantify the Geroch mass. If the
constructed Riemannian three-space happens to be asymptotically flat and the
$\rho$-integral of the integrodifferential expression is non-negative, then not
only the positive mass theorem but, if one of the $\mathscr{S}_{\rho}$ level
sets is a minimal surface, the Penrose inequality also holds. Notably, neither
of the above results requires the scalar curvature of the constructed
three-metric to be non-negative.
