  Using Seiberg-Witten theory, it is shown that any Kaehler metric of constant
negative scalar curvature on a compact 4-manifold M minimizes the L^2-norm of
scalar curvature among Riemannian metrics compatible with a fixed decomposition
H^2(M)=(H^+) + (H^-). This implies, for example, that any such metric on a
minimal ruled surface must be locally symmetric.
