On the existence of non-trivial laminations in $mathbb{CP}^2$

In this article, we show the existence of a nontrivial Riemann surface lamination embedded in $mathbb{CP}^2$ by using Donaldsons construction of asymptotically holomorphic submanifolds. Further, the lamination we obtain has the property that each leaf is a totally geodesic submanifold of $mathbb{CP}^2 $ with respect to the Fubini-Study metric. This may constitute a step in understanding the conjecture on the existence of minimal exceptional sets in $mathbb{CP}^2$.