Title: Seiberg Witten Invariants and Uniformizations.

Abstract:

    We study the Seiberg Witten equations and its applications in
uniformization problems.
First, we show that Kahler surfaces covered by product of disks can be
characterized
using negative Seiberg Witten invariant.

    Second, we shall use Seiberg Witten equations to construct projectively
flat U(2,1) connections
on Einstein manifolds and uniformize those with optimal Chern numbers.

    Third, we study \Omega^2_- invariant solutions for U(2,1) perturbed
anti-self-dual equations
and show that it  decouples to the Seiberg Witten equations and Einstein
equations.