Seiberg-Witten equations on certain manifolds with cusps

摘要

We study the Seiberg-Witten equations on noncompact manifolds diffeomorphic to the product of two hyperbolic Riemann surfaces.First, we show how to construct irreducible solutions of theSeiberg-Witten equations for any metric of finite volume which has a"nice'' behavior at infinity. Then we compute the infimum of theL2-norm of scalar curvature on these spaces and givenonexistence results for Einstein metrics on blow-ups. Thisgeneralizes to the finite volume setting some well-known results ofLeBrun.