# Pfaff systems, currents and hulls

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Nessim Sibony

created by risa on 27 Oct 2015

9 nov 2015
-- 15:00

Aula D'Antoni, Dip. Matematica, UniversitĂ "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-AmpĂ¨re type. We also discuss extension
problems of positive directed currents.