AbstractLet X be a compact Kähler manifold. Let $$T_1, \ldots , T_m$$
T
1
,
…
,
T
m
be closed positive currents of bi-degree (1, 1) on X and T an arbitrary closed positive current on X. We introduce the non-pluripolar product relative to T of $$T_1, \ldots , T_m$$
T
1
,
…
,
T
m
. We recover the well-known non-pluripolar product of $$T_1, \ldots , T_m$$
T
1
,
…
,
T
m
when T is the current of integration along X. Our main results are a monotonicity property of relative non-pluripolar products, a necessary condition for currents to be of relative full mass intersection in terms of Lelong numbers, and the convexity of weighted classes of currents of relative full mass intersection. The former two results are new even when T is the current of integration along X.
An extremal problem for generalized Lelong numbers
