Further remarks on the higher dimensional Suita conjecture

Abstract

For a domain $D\subset {\mathbb{C}}^n$, $n\ge 2$, let $F_D^k(z)=K_D(z)\lambda (I_D^k(z))$, where $K_D(z)$ is the Bergman kernel of $D$ along the diagonal and $\lambda (I_D^k(z))$ is the Lebesgue measure of the Kobayashi indicatrix at the point $z$. This biholomorphic invariant was introduced by B\locki and in this note, we study its limiting boundary behaviour on two classes of domains namely, $h$-extendible and strongly pseudoconvex polyhedral domains.

15 pages