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Further remarks on the higher dimensional Suita conjecture

Volume 125 / 2020

G. P. Balakumar, Diganta Borah, Prachi Mahajan, Kaushal Verma Annales Polonici Mathematici 125 (2020), 101-115 MSC: 32F45, 32A07, 32A25. DOI: 10.4064/ap200203-21-4 Published online: 9 July 2020

Abstract

For a domain $D \subset \mathbb C^n$, $n \ge 2$, let $F^k_D(z)=K_D(z)\lambda (I^k_D(z))$, where $K_D(z)$ is the Bergman kernel of $D$ along the diagonal and $\lambda (I^k_D(z))$ 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.

Authors

  • G. P. BalakumarDepartment of Mathematics
    Indian Institute of Technology Palakkad
    Palakkad 678557, India
    e-mail
  • Diganta BorahIndian Institute of
    Science Education and Research
    Pune 411008, India
    e-mail
  • Prachi MahajanDepartment of Mathematics
    Indian Institute of Technology Bombay
    Powai, Mumbai 400076, India
    e-mail
  • Kaushal VermaDepartment of Mathematics
    Indian Institute of Science
    Bangalore 560 012, India
    e-mail

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