广义环上Bergman核的多重次调和性
Plurisubharmonicity of Bergman Kernels on generalized annuli
摘要：
设$A_ζ=Ω-\overline{ρ(ζ)\cdotΩ}$是整环$U$上的广义环族.证明了在$ρ\in PSH(U)$的条件下，$A_ζ$的Bergman核$K_ζ(z)$的对数$\log K_ζ(z)$是多重次调和的.值得注意的是，当$A_ζ$的维数大于1时，$A_ζ$是非伪凸的.对于${\mathbb C}$中的标准环，我们得到了一个有趣的$\partial^2 \log K_ζ/\partial ζ\partial\barζ$公式，以及它的边界表现。
英文摘要：
Let $A_ζ=Ω-\overline{ρ(ζ)\cdotΩ}$ be a family of generalized annuli over a domain $U$. We show that the logarithm $\log K_ζ(z)$ of the Bergman kernel $K_ζ(z)$ of $A_ζ$ is plurisubharmonic provided $ρ\in PSH(U)$. It is remarkable that $A_ζ$ is non-pseudoconvex when the dimension of $A_ζ$ is larger than one. For standard annuli in ${\mathbb C}$, we obtain an interesting formula for $\partial^2 \log K_ζ/\partial ζ\partial\barζ$, as well as its boundary behavior.
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。
