Further remarks on the higher dimensional Suita conjecture

Abstract

For a domain D⊂Cn, n≥2, let FkD(z)=KD(z)λ(IkD(z)), where KD(z) is the Bergman kernel of D along the diagonal and λ(IkD(z)) is the Lebesgue measure of the Kobayashi indicatrix at the point z. This biholomorphic invariant was introduced by Błocki. We study its limiting boundary behaviour on two classes of domains: h-extendible and strongly pseudoconvex polyhedral domains.