Lower bounds on the Bergman metric near a point of finite type. (English) Zbl 0764.32006

This paper determines lower bounds on the rate of blow-up of the Bergman metric on a smoothly bounded domain \(\Omega\) near a finite type boundary point \(p\). The rate of blow-up is directly connected to the order of smoothing of the \(\overline\partial\)-Neumann problem near \(p\); this in turn (according to work of Catlin) is related to the D’Angelo type of \(p\).
The paper contains interesting results concerning localization of the metric.


32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32H99 Holomorphic mappings and correspondences
32A10 Holomorphic functions of several complex variables
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
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