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arXiv · 1808.08007

Remarks on the higher dimensional Suita conjecture

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

To study the analog of Suita's conjecture for domains $D \subset \mathbb{C}^n$, $n \ge 2$, B\l ocki introduced the invariant $F^k_D(z)=K_D(z)\lambda\big(I^k_D(z)\big)$, 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 $z$. In this note, we study the behaviour of $F^k_D(z)$ (and other similar invariants using different metrics) on strongly pseudconvex domains and also compute its limiting behaviour explicitly at certain points of decoupled egg domains in $\mathbb{C}^2$.

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G. P. Balakumar, Diganta Borah, Prachi Mahajan, Kaushal Verma. 2018-08-24. Remarks on the higher dimensional Suita conjecture. https://arxiv.org/abs/1808.08007

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