  We introduce a class of "weakly asymptotically hyperbolic" geometries whose
sectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$,
conformally compact. We subsequently investigate the rate at which curvature
invariants decay at infinity, identifying a conformally invariant tensor which
serves as an obstruction to "higher order decay" of the Riemann curvature
operator. Finally, we establish Fredholm results for geometric elliptic
operators, extending the work of Rafe Mazzeo and John M. Lee to this setting.
As an application, we show that any weakly asymptotically hyperbolic metric is
conformally related to a weakly asymptotically hyperbolic metric of constant
negative curvature.
