Proposition 2.1 . [028A]

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Proposition 2.1.

Let $V$ be a compact Kähler manifold equipped with a Kähler form $\omega$ , and let $X$ be a complex submanifold of $V$ . Then

PSH^{+}(X,\omega\,|_{{}_{X}})\cap{\mathcal{C}}^{\infty}(X,{\mathbb{R}})=\left(PSH^{+}(V,\omega)\cap{\mathcal{C}}^{\infty}(V,\mathbb{R})\right)\,|_{{}_{X}}.