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

McNeal, Jeffery D.

Ann. Math. (2) 136, No. 2, 339-360 (1992).

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.

Reviewer: S.G.Krantz (St.Louis)

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