Further remarks on the higher dimensional Suita conjecture. (arXiv:1812.03010v1 [math.CV])

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\l ocki and in this note, we study the boundary behaviour of $F^k_D(z)$ near a finite type boundary point where the boundary is smooth, pseudoconvex with the corank of its Levi form being at most $1$. We also compute its limiting behaviour near the boundary of certain other basic classes of domains.查看全文

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