  We show that the S^1-equivariant Yamabe invariant of the 3-sphere, endowed
with the Hopf action, is equal to the (non-equivariant) Yamabe invariant of the
3-sphere. More generally, we establish a topological upper bound for the
S^1-equivariant Yamabe invariant of any closed oriented 3-manifold endowed with
an S^1-action. Furthermore, we prove a convergence result for the equivariant
Yamabe constants of an accumulating sequence of subgroups of a compact Lie
group acting on a closed manifold.
