On the pluricomplex Poisson kernel and the associated complex Monge--Ampère equation

We give a geometric characterization of the pluricomplex Poisson kernel of bounded strongly linearly convex domains in $\mathbb C^{n+1}$ in terms of their foliation by all complex geodesic discs whose closure contains a fixed boundary point, thus confirming a conjecture posed by Bracci et al. in 200