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arXiv · 1812.03010

Further remarks on the higher dimensional Suita conjecture

G. P. Balakumar·Diganta Borah·Prachi Mahajan·Kaushal Verma
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Abstract

For a domain $D \subset \mathbb C^n$, $n \ge 2$, let $F^k_D(z)=K_D(z)\lambda\big(I^k_D(z)\big)$, where $K_D(z)$ is the Bergman kernel of $D$ along the diagonal and $\lambda\big(I^k_D(z)\big)$ 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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G. P. Balakumar, Diganta Borah, Prachi Mahajan, Kaushal Verma. 2018-12-07. Further remarks on the higher dimensional Suita conjecture. https://arxiv.org/abs/1812.03010

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