Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains

dc.creatorBerndtsson, Bo
dc.date2005-05-23
dc.date.accessioned2026-07-07T05:20:09Z
dc.date.available2026-07-07T05:20:09Z
dc.descriptionLet $D$ 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.identifierhttps://arxiv.org/abs/math/0505469
dc.identifierhttp://arxiv.org/abs/math/0505469
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75277
dc.subjectComplex Variables
dc.subjectAlgebraic Geometry
dc.subject32E
dc.titleSubharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains
dc.typetext

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