  Let $M$ be a complete simply connected manifold which is in addition Gromov
hyperbolic, coercive and roughly starlike. For a given harmonic function on
$M$, a local Fatou Theorem and a pointwise criteria of non-tangential
convergence coming from the density of energy are shown: at almost all points
of the boundary, the harmonic function converges non-tangentially if and only
if the supremum of the density of energy is finite. As an application of these
results, a Calder\'on-Stein Theorem is proved, that is, the non-tangential
properties of convergence, boundedness and finiteness of energy are equivalent
at almost every point of the boundary.
