  We show various sharp Hardy-type inequalities for the linear and quasi-linear
Laplacian on non-compact harmonic manifolds with a particular focus on the case
of Damek-Ricci spaces. Our methods make use of the optimality theory developed
by Devyver/Fraas/Pinchover and Devyver/Pinchover and are motivated by
corresponding results for hyperbolic spaces by Berchio/Ganguly/Grillo, and
Berchio/Ganguly/Grillo/Pinchover.
