Strict plurisubharmonicity of Bergman kernels on generalized annuli
Volume 111 / 2014
Annales Polonici Mathematici 111 (2014), 237-243
MSC: Primary 32A25; Secondary 32U05.
DOI: 10.4064/ap111-3-2
Abstract
Let be a family of generalized annuli over a domain U. We show that the logarithm of the Bergman kernel K_{\zeta}(z) of A_\zeta is plurisubharmonic provided \rho\in {\rm PSH}(U). It is remarkable that A_\zeta is non-pseudoconvex when the dimension of A_\zeta is larger than one. For standard annuli in {\mathbb C}, we obtain an interesting formula for \partial^2 \log K_{\zeta}/\partial \zeta\partial\bar{\zeta}, as well as its boundary behavior.