In this paper, we improve a result by Chodosh and Ketover . We prove that, in an asymptotically flat $3$-manifold $M$ that contains no closed minimal surfaces, fixing $q \in M$ and $V$ a $2$-plane in $T_q M$ there is a properly embedded minimal plane $\Sigma$ in $M$ such that $q \in \Sigma$ and $T_q \Sigma = V$. We also prove that fixing three points in $M$ there is a properly embedded minimal plane passing through these three points.
"Minimal planes in asymptotically flat three-manifolds." J. Differential Geom. 120 (3) 533 - 556, March 2022. https://doi.org/10.4310/jdg/1649953568