Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains
| dc.creator | Berndtsson, Bo | |
| dc.date | 2005-05-23 | |
| dc.date.accessioned | 2026-07-07T05:20:09Z | |
| dc.date.available | 2026-07-07T05:20:09Z | |
| dc.description | Let $D$ be a pseudoconvex domain in $\C^k_t\times\Cn_z$ and let $ϕ$ be a plurisubharmonic function in $D$. For each $t$ we consider the $n$-dimensional slice of $D$, $D_t=\{z; (t,z)\in D\}$, let $ϕ^t$ be the restriction of $ϕ$ to $D_t$ and denote by $K_t(z,ζ)$ the Bergman kernel of $D_t$ with the weight function $ϕ^t$. Generalizing a recent result of Maitani and Yamaguchi (corresponding to $n=1$ and $ϕ=0$) we prove that $\log K_t(z,z)$ is a plurisubharmonic function in $D$. We also generalize an earlier results of Yamaguchi concerning the Robin function and discuss similar results in the setting of $\Rn$. | |
| dc.identifier | https://arxiv.org/abs/math/0505469 | |
| dc.identifier | http://arxiv.org/abs/math/0505469 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75277 | |
| dc.subject | Complex Variables | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32E | |
| dc.title | Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains | |
| dc.type | text |