  In this paper we provide a way of taking $L^p$, $p > \frac{m}{2}$ bounds on a
$m-$ dimensional Riemannian metric and transforming that into H\"{o}lder bounds
for the corresponding distance function. One can think of this new estimate as
a type of Morrey inequality for Riemannian manifolds where one thinks of a
Riemannian metric as the gradient of the corresponding distance function so
that the $L^p$, $p > \frac{m}{2}$ bound analogously implies H\"{o}lder control
on the distance function. This new estimate is then used to state a compactness
theorem, another theorem which guarantees convergence to a particular
Riemmanian manifold, and a new scalar torus stability result. We expect these
results to be useful for proving geometric stability results in the presence of
scalar curvature bounds when Gromov-Hausdorff convergence is expected.
