关于高维Suita猜想的注记
Remarks on the higher dimensional Suita conjecture
摘要：
为了研究Suita猜想对域$D \subset \mathbb{C}^n$、$n \ge 2$的类似物，Besiocki引入了不变量$F^k_D(z)=K_D(z)λ\big(I^k_D(z)\big)$，其中$K_D(z)$是$D$沿对角线的Bergman核，而$λ\big(I^k_D(z)\big)$是小林指示线在点$z$的勒贝格测度。本文研究了强伪凸域上$F^k_D(z)$（以及其他使用不同度量的类似不变量）的行为，并计算了它在$\mathbb{C}^2$中解耦蛋域的某些点上的极限行为.
英文摘要：
To study the analog of Suita's conjecture for domains $D \subset \mathbb{C}^n$, $n \ge 2$, Błocki introduced the invariant $F^k_D(z)=K_D(z)λ\big(I^k_D(z)\big)$, where $K_D(z)$ is the Bergman kernel of $D$ along the diagonal and $λ\big(I^k_D(z)\big)$ 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 $\mathbb{C}^2$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
