WEYL CURVATURE, EINSTEIN-METRICS, AND SEIBERG-WITTEN THEORY

We show that solutions of the Seiberg-Witten equations lead to nontriv ial estimates for the L-2-norm of the Weyl curvature of a compact Riem annian 4-manifold. These estimates are then used to derive new obstruc tions to the existence of Einstein metrics on smooth compact 4-manifol ds with a non-zero Seiberg-Witten invariant. These results considerabl y refine those previously obtained [21] by using scalar-curvature esti mates alone.