We consider the self-dual conformal classes on n#CP^2 discovered by LeBrun.
These depend upon a choice of n points in hyperbolic 3-space, called monopole
points. We investigate the limiting behavior of various constant scalar
curvature metrics in these conformal classes as the points approach each other,
or as the points tend to the boundary of hyperbolic space. There is a close
connection to the orbifold Yamabe problem, which we show is not always solvable
(in contrast to the case of compact manifolds). In particular, we show that
there is no constant scalar curvature orbifold metric in the conformal class of
a conformally compactified non-flat hyperkahler ALE space in dimension four.Comment: 34 pages, to appear in Annales de L'Institut Fourie
