  Let $n \geq 4$ and let $\Omega$ be a bounded hyperconvex domain in
$\mathbb{C}^{n}$. Let $\varphi$ be a negative exhaustive smooth
plurisubharmonic function on $\Omega$. We show that any holomorphic function
defined on a connected open neighborhood of the support of $(i\partial
\overline{\partial}\varphi)^{n-3}$ can be extended to the holomorphic function
on $\Omega$.
