Pluripotential theory and Monge-Ampère foliations

After reviewing basic notions on Monge- Ampère foliations, it is discussed the construction of modular data for complex manifolds which carry regular pluricomplex Green functions, class of manifolds which includes all smoothly bounded, strictly linearly convex domains and all smoothly bounded, strongly pseudoconvex circular domains of Cn. It is given a up to date report on the problem of defining pluricomplex Green functions in the almost complex setting, providing sufficient conditions on almost complex structures, which ensure existence of almost complex Green pluripotentials and equality between the notions of stationary disks and of Kobayashi extremal disks, and allow extensions of known results to the case of non integrable complex structures.