The Bergman-Fridman invariant on some classes of pseudoconvex domains

We study the boundary behaviour of a variant of the Fridman’s invariant function (defined in terms of the Bergman metric) on Levi corank one domains, strongly pseudoconvex domains, smoothly bounded convex domains in ${\mathbb{C}}^n$ and polyhedral domains in ${\mathbb{C}}^2$.