Pluripotential Theory and Monge–Ampère Foliations

摘要: A regular, rank one solution u of the complex homogeneous Monge–Ampere equation \({(\partial \overline{\partial }u)}^{n} = 0\) on a manifold is associated with foliation, given by curves along which harmonic. foliations find many applications in geometry and selection good candidate for foliation always first step construction well behaved solutions equation. Here, after reviewing some basic notions foliations, we concentrate two main topics. We discuss (complete) modular data large family manifolds, carry regular pluricomplex Green functions. This class manifolds naturally includes all smoothly bounded, strictly linearly convex domains strongly pseudoconvex circular \({\mathbb{C}}^{n}\). then report problem defining functions almost setting, providing sufficient conditions structures, ensure existence pluripotentials equality between stationary disks Kobayashi extremal disks, allow extensions known results to case non integrable structures.