Boundary behaviour of the Bergman invariant and related quantities (Q926308)

The boundary behaviour of the Bergman kernel has been known since the 1974 seminal work of Fefferman. Using Fefferman's classical result on the boundary singularity of the Bergman kernel, this paper gives an analogous complete description of the boundary singularity of various related quantities like the Bergman invariant, the coefficients of the Bergman metric, of the associated Laplace-Beltrami operator, of its curvature tensor, Ricci curvature and scalar curvature. The main point is that even though one would expect a bit stronger singularities than the one for the Bergman kernel, due to the differentiations involved, all these quantities turn out to have -- except for a different leading power of the defining function -- the same kind of singularity as the solution of the Monge-Ampère equation.