  We prove the existence of a quantum isometry groups for new classes of metric
spaces: (i) geodesic metrics for compact connected Riemannian manifolds
(possibly with boundary) and (ii) metric spaces admitting a uniformly
distributed probability measure. In the former case it also follows from recent
results of the second author that the quantum isometry group is classical, i.e.
the commutative $C^*$-algebra of continuous functions on the Riemannian
isometry group.
