9 nov 2015 -- 15:00
Aula D'Antoni, Dip. Matematica, Università "Tor Vergata", Roma
Abstract.
Let S be a Pfaff system of dimension 1, on a compact complex manifold M. We prove that there is a positive ddbar closed current T of mass 1 directed by the Pfaff system S. There is no integrability assumption. We also show that local singular solutions exist always.
Using i\ddbar-negative currents, we discuss Jensen measures, local maximum principle and hulls with respect to a cone P of smooth functions in the Euclidean complex space, subharmonic in some directions. The case where P is the cone of plurisubharmonic functions is classical. We use the results to describe the harmonicity properties of the solutions of equations of homogeneous, Monge-Ampère type. We also discuss extension problems of positive directed currents.