A Priori Estimates for the Homogeneous Monge-Ampère Equation on Kähler Manifolds

<div>This thesis investigates the existence of smooth solutions to MA(<i>F</i>), proving a priori estimates on the leaves of the foliation that corresponds to smooth solutions. We demonstrate that sequences of leaves of Monge-Amp`ere foliations converge to holomorphic disks.</div>