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

الأصل · EN

This paper studies Fefferman's program F3 of expressing the singularity of the Bergman kernel, for smoothly bounded strictly pseudoconvex domains Ω⊂ⁿ, in terms of local biholomorphic invariants of the boundary. By F1, the Bergman kernel on the diagonal K(z,cz) is written in the form K=ϕr⁻ⁿ⁻¹+ψ r with ϕ,ψ∈ C∞(Ω), where r is a (smooth) defining function of Ω. Recently, Bailey, Eastwood and Graham BEG, building on Fefferman's earlier work 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 r.