  Recently, Einsiedler and the authors provided a bound in terms of escape of
mass for the amount by which upper-semicontinuity for metric entropy fails for
diagonal flows on homogeneous spaces $\Gamma\backslash G$, where $G$ is any
connected semisimple Lie group of real rank 1 with finite center and $\Gamma$
is any nonuniform lattice in $G$. We show that this bound is sharp and apply
the methods used to establish bounds for the Hausdorff dimension of the set of
points which diverge on average.
