  We prove that every Einstein metric on the unit ball B^4 of C^2, asymptotic
to the Bergman metric, is equal to it up to a diffeomorphism. We need a
solution of Seiberg--Witten equations in this infinite volume setting.
Therefore, and more generally, if M^4 is a manifold with a CR-boundary at
infinity, an adapted spinc-structure which has a non zero Kronheimer--Mrowka
invariant and an asymptotically complex hyperbolic Einstein metric, we produce
a solution of Seiberg--Witten equations with an strong exponential decay
property.
