Construction of boundary invariants and the logarithmic singularity of the Bergman kernel
| dc.creator | Hirachi, Kengo | |
| dc.date | 2000-10-02 | |
| dc.date.accessioned | 2026-07-07T04:37:47Z | |
| dc.date.available | 2026-07-07T04:37:47Z | |
| dc.description | This 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.description | 41 pages | |
| dc.identifier | https://arxiv.org/abs/math/0010014 | |
| dc.identifier | http://arxiv.org/abs/math/0010014 | |
| dc.identifier | Ann. of Math. (2) 151 (2000), no. 1, 151--191 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60030 | |
| dc.subject | Complex Variables | |
| dc.subject | 32Axx (Primary); 46Exx, 46N20 (Secondary) | |
| dc.title | Construction of boundary invariants and the logarithmic singularity of the Bergman kernel | |
| dc.type | text |