On the extension of Kähler currents on compact complex manifolds

Abstract

Let $(X,\omega )$ be a compact Kähler manifold and let $V\subset X$ be a closed complex submanifold. Coman-Guedj-Zeriahi proposed the problem: is every $\omega {|}_V$-plurisubharmonic function on $V$ the restriction of an $\omega$-plurisubharmonic function on $X$? In this paper, we solve this problem affirmatively, even for a compact Hermitian manifold.

9 pages, comments welcome