  The geodesic distance vanishes on the group of compactly supported
diffeomorphisms of a Riemannian manifold $M$ of bounded geometry, for the right
invariant weak Riemannian metric which is induced by the Sobolev metric $H^s$
of order $0\le s<\tfrac12$ on the Lie algebra $\mathfrak X_c(M)$ of vector
fields with compact support.
