Abstract.
Using Fefferman’s classical result on the boundary singularity of the Bergman kernel, we give an analogous description of the boundary behaviour 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-Ampére equation.
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Author’s addresses: Mathematics Institute, Silesian University at Opava, Na Rybníčku 1, 74601 Opava, Czech Republic and Mathematics Institute, Žitná 25, 11567 Prague 1, Czech Republic
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Engliš, M. Boundary behaviour of the Bergman invariant and related quantities. Monatsh Math 154, 19–37 (2008). https://doi.org/10.1007/s00605-008-0522-8
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DOI: https://doi.org/10.1007/s00605-008-0522-8