Theorem 2.2 . [028D]

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Theorem 2.2.

Let $X$ be a subvariety of a projective manifold $V$ equipped with a Hodge form $\omega$ . If $\varphi\in PSH(X,\omega\,|_{{}_{X}})$ then given any constant $a>0$ there exists $\psi\in PSH(V,\omega)$ so that $\psi\,|_{{}_{X}}=\varphi$ and $\max_{V}\psi<\max_{X}\varphi+a$ .