Boundary Distance Functions of Unramified Riemann Domains over \(\mathbb {C}^n\)

Let \((D, \pi )\) $(D,\pi )$ be an unramified Riemann domain over \(\mathbb {C}^n\) ${\mathbb{C}}^n$ and let d denote the boundary distance function of \((D, \pi )\) $(D,\pi )$ with respect to an arbitrary complex norm on \(\mathbb {C}^n\) ${\mathbb{C}}^n$ . Then, we prove that the function \(-\ln d\) $-lnd$ is subpluriharmonic in the sense of Fujita on D.