Further remarks on the higher dimensional Suita conjecture

2018/12/07 by G. P. Balakumar, Diganta Borah, Balakumar, G. P. +5
Mathematics · #32A07 #32A25 #32F45 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1812.03010

openalex publication_date 2018/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a domain D ⊂ \mathbb Cⁿ, n ≥ 2, let F^k_D(z)=K_D(z)λ(I^k_D(z)), where K_D(z) is the Bergman kernel of D along the diagonal and λ(I^k_D(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.

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