## 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.

### MSC:

 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

### Keywords:

subelliptic estimate; Bergman metric; finite type
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