  In this paper, we study a geometric property of a continuous plurisubharmonic
function which is a solution of the Monge-Amp\`ere equation and has a convex
level set. To prove our main theorem, we show a minimum principle of a maximal
plurisubharmonic function. By using our results and Lempert's results, we show
a relation between the supports of the Monge-Amp\`ere currents and complex
$k$-extreme points of closed balls for the Kobayashi distance in a bounded
convex domain in $\mathbb{C}^{n}$.
