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Construction of boundary invariants and the logarithmic singularity of the Bergman kernel. (English) Zbl 0954.32002

The author studies Fefferman’s program of expressing the singularity of the Bergman kernel for smoothly bounded strictly pseudoconvex domains \(\Omega\subset \mathbb C^n\) in terms of local biholomorphic invariants of the boundary. The Bergman kernel on the diagonal \(K(z,\overline{z})\) is written in the form \(K=\varphi r^{-n-1}+\psi\log r\) with \(\varphi,\psi\in C^\infty(\overline{\Omega}),\) where \(r\) is a smooth defining function of \(\Omega.\)
The purpose of this paper is to give a full invariant expression of the weak singularity \(\psi\log r.\)

MSC:

32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
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