Construction of boundary invariants and the logarithmic singularity of the Bergman kernel

dc.creatorHirachi, Kengo
dc.date2000-10-02
dc.date.accessioned2026-07-07T04:37:47Z
dc.date.available2026-07-07T04:37:47Z
dc.descriptionThis paper studies Fefferman's program \cite{F3} of expressing the singularity of the Bergman kernel, for smoothly bounded strictly pseudoconvex domains $Ω\subset\C^n$, in terms of local biholomorphic invariants of the boundary. By \cite{F1}, the Bergman kernel on the diagonal $K(z,cz)$ is written in the form $$ K=ϕr^{-n-1}+ψ\log r \qtext{with} ϕ,ψ\in C^\infty(\cΩ), $$ where $r$ is a (smooth) defining function of $Ω$. Recently, Bailey, Eastwood and Graham \cite{BEG}, building on Fefferman's earlier work \cite{F3}, obtained a full invariant expression of the strong singularity $ϕr^{-n-1}$. The purpose of this paper is to give a full invariant expression of the weak singularity $ψ\log r$.
dc.description41 pages
dc.identifierhttps://arxiv.org/abs/math/0010014
dc.identifierhttp://arxiv.org/abs/math/0010014
dc.identifierAnn. of Math. (2) 151 (2000), no. 1, 151--191
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60030
dc.subjectComplex Variables
dc.subject32Axx (Primary); 46Exx, 46N20 (Secondary)
dc.titleConstruction of boundary invariants and the logarithmic singularity of the Bergman kernel
dc.typetext

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